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-2.08 ms +- 28.1 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-3.56 ms +- 35.6 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+1.17 ms +- 17 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+2.06 ms +- 46.3 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-1.05 ms +- 16.1 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-2.52 ms +- 26.2 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+520 us +- 9.69 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+1.36 ms +- 10.7 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-3.55 ms +- 32.8 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-7.17 ms +- 38 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+2.13 ms +- 19.2 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+4.13 ms +- 18.5 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([0.31372568, 0.72167143, 0.11277527])\n+Out[7]: array([0.20177295, 0.80481925, 0.25923581])\n \n In [8]: rng.random(3, dtype=np.float32)\n-Out[8]: array([0.1022529 , 0.65221405, 0.698686 ], dtype=float32)\n+Out[8]: array([0.6782615 , 0.70966625, 0.8387832 ], dtype=float32)\n \n In [9]: rng.integers(0, 256, size=3, dtype=np.uint8)\n-Out[9]: array([102, 67, 157], dtype=uint8)\n+Out[9]: array([ 82, 164, 39], 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([0.90602207, 0.89725564])\n+Out[12]: array([0.56660927, 0.68786807])\n \n In [13]: print(existing)\n-[0.90602207 0.89725564 0. 0. ]\n+[0.56660927 0.68786807 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([1.13434729, 0.01956587])\n+Out[4]: array([ 1.0984877 , -0.06986567])\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([5.12412867, 5.1045628 ], domain=[0., 9.], window=[-1., 1.], symbol='x')\n+Out[6]: Polynomial([4.87332896, 4.94319463], 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([0.01956587, 1.13434729], domain=[-1., 1.], window=[-1., 1.], symbol='x')\n+Out[7]: Polynomial([-0.06986567, 1.0984877 ], 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([1.13434729, 0.01956587])\n+Out[4]: array([ 1.0984877 , -0.06986567])\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([5.12412867, 5.1045628 ], domain=[0., 9.], window=[-1.,\n+Out[6]: Polynomial([4.87332896, 4.94319463], 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([0.01956587, 1.13434729], domain=[-1., 1.], window=[-1.,\n+Out[7]: Polynomial([-0.06986567, 1.0984877 ], 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": "@@ -32346,15 +32346,14 @@\n \"01280782\": [2335, 2378, 2425],\n \"016\": [648, 653],\n \"01652764\": 2634,\n \"01666667\": 1544,\n \"016j\": 2105,\n \"01831564\": 1660,\n \"018318\": [2353, 2400, 2450],\n- \"01956587\": 2488,\n \"01j\": 514,\n \"01t00\": [55, 62, 361, 2525],\n \"01t08\": 2525,\n \"01t12\": 55,\n \"02\": [54, 55, 147, 162, 163, 410, 547, 566, 669, 1335, 1586, 1601, 1658, 1715, 1772, 1816, 1829, 1885, 2104],\n \"020995\": 57,\n \"02284196\": 1697,\n@@ -32380,36 +32379,37 @@\n \"04\": [54, 55, 164, 410, 547, 1586, 2463, 2594, 2658],\n \"0400\": 360,\n \"04097352\": 2634,\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, 2461, 2647],\n+ \"05\": [55, 91, 163, 410, 548, 669, 896, 1095, 1871, 2083, 2173, 2353, 2400, 2450, 2647],\n \"0500\": 360,\n \"05093587\": 2634,\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+ \"06986567\": 2488,\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, 2654],\n- \"08\": [55, 91, 147, 410, 523, 548, 896, 1095, 2322, 2366, 2413, 2461, 2525, 2658],\n+ \"08\": [55, 91, 147, 410, 523, 548, 896, 1095, 2322, 2366, 2413, 2525, 2658],\n \"0800\": 2525,\n \"08187135\": 54,\n \"08333333\": [1645, 1871],\n \"08405657\": 1867,\n \"0855\": 2641,\n \"08553692\": 38,\n \"085537\": 2641,\n@@ -32418,14 +32418,15 @@\n \"08703704\": [1113, 1543],\n \"087300000000000003\": [2346, 2392, 2441],\n \"09\": [55, 2171, 2252, 2323, 2367, 2414],\n \"090097550553843\": 2641,\n \"09417735\": [349, 2457, 2638],\n \"0943951\": 1911,\n \"09640474436813\": 675,\n+ \"0984877\": 2488,\n \"09861229\": [657, 2654],\n \"0999755859375\": 62,\n \"099975586\": 62,\n \"0a1\": 577,\n \"0a2\": 577,\n \"0b00000011\": [1519, 2235],\n \"0b1\": [34, 50, 577, 2602],\n@@ -32496,16 +32497,15 @@\n \"100j\": 1909,\n \"100x5\": 652,\n \"101\": [86, 137, 138, 143, 145, 570, 1325, 2077, 2463, 2665],\n \"1010\": [145, 1519, 2077],\n \"10100\": [143, 570],\n \"1015\": 2592,\n \"10151\": 2560,\n- \"102\": [2461, 2463, 2636, 2665],\n- \"1022529\": 2461,\n+ \"102\": [2463, 2636, 2665],\n \"1023\": [141, 2583],\n \"1024\": [66, 72, 2657],\n \"10240\": 977,\n \"103\": 2463,\n \"10330\": 55,\n \"10339\": [2536, 2542],\n \"1035\": [1643, 1655],\n@@ -32519,15 +32519,14 @@\n \"10401\": 2536,\n \"10403\": 2536,\n \"10412\": 2536,\n \"10424\": 2536,\n \"10425\": 2536,\n \"10431\": 2536,\n \"10435\": 2536,\n- \"1045628\": 2488,\n \"1049\": 2098,\n \"105\": 2463,\n \"10534\": 2536,\n \"10536\": 2536,\n \"10537\": 2536,\n \"10539\": 2536,\n \"10540\": 2536,\n@@ -32609,15 +32608,14 @@\n \"11203\": 2539,\n \"11210\": 2542,\n \"11211\": 2539,\n \"11218\": 2542,\n \"11219\": 2539,\n \"11251\": 2539,\n \"11274\": 2540,\n- \"11277527\": 2461,\n \"11294\": 2540,\n \"113\": [674, 2463, 2665],\n \"11308\": 2542,\n \"1138\": 2612,\n \"114\": 2463,\n \"11407192\": 1822,\n \"1142\": [2353, 2400, 2450],\n@@ -32716,15 +32714,14 @@\n \"123456789a12\": 25,\n \"123456789a123456789b\": 25,\n \"1234567e\": 2172,\n \"12346\": 2462,\n \"1235\": 2091,\n \"123abc\": [302, 305, 2131, 2134],\n \"124\": [98, 905],\n- \"12412867\": 2488,\n \"125\": [470, 660, 1114, 1142, 1645, 1651, 1899, 1900, 2239, 2339, 2382, 2429, 2460, 2491, 2658, 2665],\n \"12589991e\": 645,\n \"126\": [863, 1048, 1116, 1904],\n \"1261\": 2612,\n \"12658\": 2560,\n \"12697628\": 2634,\n \"127\": [62, 66, 514, 863, 1048, 1102, 1116, 1904, 2301, 2302, 2462, 2463, 2464, 2583, 2638],\n@@ -32760,15 +32757,14 @@\n \"133\": [527, 2330, 2374, 2421],\n \"13392\": 2551,\n \"13394\": 2551,\n \"13396\": 2551,\n \"134\": [542, 968, 969],\n \"13406828\": 2458,\n \"13421\": 2566,\n- \"13434729\": 2488,\n \"1344\": [270, 880, 1069, 1229, 1312, 1466, 1986],\n \"13450292\": 54,\n \"135\": [105, 130],\n \"13516\": 2572,\n \"13523\": 2551,\n \"13533528\": 1774,\n \"13549\": 2551,\n@@ -33032,15 +33028,15 @@\n \"15648\": 2566,\n \"15666\": 2572,\n \"15675\": 2562,\n \"15676\": 2562,\n \"15677\": 2562,\n \"15679\": 2562,\n \"15685\": 2566,\n- \"157\": [2461, 2463],\n+ \"157\": 2463,\n \"15715\": 2566,\n \"15722\": 2562,\n \"15729\": 2562,\n \"1573\": 2612,\n \"15734\": 2562,\n \"15759\": 2572,\n \"15769\": 2566,\n@@ -33103,15 +33099,15 @@\n \"16200\": 2572,\n \"1621\": [1913, 2236],\n \"1622776601683795\": 637,\n \"16232\": 2572,\n \"16236208e\": 2104,\n \"16350\": 2572,\n \"16354\": 2659,\n- \"164\": 675,\n+ \"164\": [675, 2461],\n \"16434881e\": 2104,\n \"16439\": 2565,\n \"16441\": 2565,\n \"16476\": 2572,\n \"16484065\": 1154,\n \"16515\": 2572,\n \"16519\": 2572,\n@@ -33554,14 +33550,15 @@\n \"2012\": [55, 162, 163],\n \"2013\": 2620,\n \"20140822061353\": [24, 32],\n \"2015\": [14, 55, 2526, 2542, 2594],\n \"2016\": [55, 557],\n \"2017\": [2533, 2534, 2612],\n \"20172\": 50,\n+ \"20177295\": 2461,\n \"2018\": [2535, 2599],\n \"2019\": [5, 42, 65, 2328, 2463, 2535, 2550, 2554, 2599, 2659],\n \"202\": [2463, 2665],\n \"2020\": [21, 55, 57, 2270, 2535, 2547, 2572, 2573],\n \"20201\": 2583,\n \"2021\": [8, 31, 42, 45, 55, 2573, 2585, 2612],\n \"20217\": 2583,\n@@ -34323,21 +34320,22 @@\n \"25802\": 2622,\n \"25812\": 2622,\n \"25816\": 2622,\n \"2584\": 28,\n \"25866\": 2622,\n \"25911\": 2622,\n \"25914\": 2622,\n+ \"25923581\": 2461,\n \"25943\": 2622,\n \"25954\": 2622,\n \"25d0\": 32,\n \"25j\": 2658,\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, 2640, 2656, 2657, 2665],\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, 2640, 2656, 2657, 2665],\n \"260\": [162, 1328, 2238, 2576, 2665],\n \"26064346e\": 147,\n \"26081\": 2625,\n \"26103\": 2625,\n \"26137788e\": 2104,\n \"26157\": 2625,\n \"262\": 2665,\n@@ -34508,15 +34506,15 @@\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, 2461, 2463, 2513, 2538, 2539, 2540, 2543, 2629, 2640, 2648, 2656, 2658, 2665],\n+ \"28\": [36, 54, 55, 146, 409, 661, 1695, 1704, 1707, 1862, 2168, 2208, 2225, 2463, 2513, 2538, 2539, 2540, 2543, 2629, 2640, 2648, 2656, 2658, 2665],\n \"28000000e\": 1335,\n \"2800000e\": 1335,\n \"28006\": 2630,\n \"28007\": 2630,\n \"2801\": 2613,\n \"28021\": 2630,\n \"28044\": 2630,\n@@ -34662,30 +34660,29 @@\n \"3125\": 2081,\n \"3128\": 2614,\n \"313\": 2665,\n \"3131\": 2614,\n \"3134\": 2614,\n \"3135\": 2614,\n \"3136\": 2614,\n- \"31372568\": 2461,\n \"314\": [420, 947],\n \"3141\": 562,\n \"3153\": 2615,\n \"31534378e\": 660,\n \"316\": [680, 1923, 2658],\n \"3160\": 2615,\n \"3168\": 2615,\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, 2636, 2638, 2640, 2644, 2645, 2647, 2648, 2651, 2656, 2657, 2658, 2665],\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, 2636, 2638, 2640, 2644, 2645, 2647, 2648, 2651, 2656, 2657, 2658, 2665],\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@@ -34731,22 +34728,22 @@\n \"34784527\": 2634,\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, 2461, 2572, 2634, 2640, 2656, 2665],\n+ \"35\": [409, 489, 669, 870, 1056, 2204, 2325, 2369, 2416, 2572, 2634, 2640, 2656, 2665],\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, 2648, 2656, 2658, 2665],\n+ \"36\": [58, 137, 355, 1752, 1761, 2204, 2225, 2323, 2367, 2414, 2461, 2463, 2491, 2536, 2648, 2656, 2658, 2665],\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@@ -34765,15 +34762,15 @@\n \"3743\": 2615,\n \"375\": [1634, 1663],\n \"37601032\": [2387, 2434],\n \"377\": 28,\n \"378\": 652,\n \"379\": 533,\n \"3793\": 2615,\n- \"38\": [59, 542, 968, 969, 1545, 1752, 1761, 2107, 2204, 2208, 2313, 2333, 2361, 2377, 2408, 2424, 2461, 2510, 2572, 2656, 2665],\n+ \"38\": [59, 542, 968, 969, 1545, 1752, 1761, 2107, 2204, 2208, 2313, 2333, 2361, 2377, 2408, 2424, 2510, 2572, 2656, 2665],\n \"380\": [2238, 2576],\n \"38268343\": 642,\n \"38268343j\": 642,\n \"3832\": 2615,\n \"38434191e\": 660,\n \"38446749\": 1867,\n \"385\": [2270, 2300],\n@@ -34782,15 +34779,15 @@\n \"3871\": 2615,\n \"38777878e\": [147, 1651],\n \"38791518e\": [421, 948],\n \"38885\": [2361, 2408],\n \"389056\": 2641,\n \"3890561\": [38, 2665],\n \"3891\": 2641,\n- \"39\": [30, 58, 2208, 2463, 2640, 2656],\n+ \"39\": [30, 58, 2208, 2461, 2463, 2640, 2656],\n \"390\": [2270, 2300],\n \"3900\": 2615,\n \"3900x\": 2463,\n \"39015\": 2316,\n \"39211752\": 1153,\n \"39337286e\": 1149,\n \"3971\": 2615,\n@@ -34926,15 +34923,15 @@\n \"4532\": [409, 661, 2168],\n \"4545724517479104\": 2460,\n \"45560727e\": 54,\n \"456\": 1921,\n \"4567\": 2643,\n \"45674898e\": 566,\n \"45a3d84\": 2521,\n- \"46\": [409, 523, 905, 1707, 2204, 2208, 2640, 2656],\n+ \"46\": [409, 523, 905, 1707, 2204, 2208, 2461, 2640, 2656],\n \"460\": [2238, 2576],\n \"46009194e\": 566,\n \"4602\": 2618,\n \"4610935\": 457,\n \"4613\": 2618,\n \"4628\": 2618,\n \"46351241j\": 2081,\n@@ -35048,15 +35045,16 @@\n \"51658839e\": 1586,\n \"517\": 10,\n \"5170\": 2620,\n \"5184\": 2620,\n \"51851852\": 1809,\n \"519928\": 2634,\n \"51992837\": 2634,\n- \"52\": [10, 50, 62, 457, 1638, 1647, 1650, 2204, 2208, 2461, 2554, 2634, 2640, 2647, 2656, 2658, 2659, 2665],\n+ \"52\": [10, 50, 62, 457, 1638, 1647, 1650, 2204, 2208, 2554, 2634, 2640, 2647, 2656, 2658, 2659, 2665],\n+ \"520\": 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@@ -35095,35 +35093,36 @@\n \"5470\": [2353, 2400, 2450],\n \"5481\": 2621,\n \"5492\": 2621,\n \"54930614\": [106, 131],\n \"5493061443340549\": [413, 619],\n \"54959369\": 2665,\n \"54999924\": 1247,\n- \"55\": [28, 59, 60, 73, 893, 1083, 1143, 1525, 1905, 2090, 2204, 2240, 2461, 2622, 2656],\n+ \"55\": [28, 59, 60, 73, 893, 1083, 1143, 1525, 1905, 2090, 2204, 2240, 2622, 2656],\n \"55000000074505806\": 1247,\n \"5510652\": 2634,\n \"55111512e\": 642,\n \"55131477\": 1153,\n \"5524\": 2621,\n \"55458479\": 349,\n \"55490914e\": 2665,\n \"5555555555555554\": 1349,\n \"55627469\": 349,\n \"55645993\": 2634,\n \"5580\": 2535,\n \"55914881e\": 2104,\n- \"56\": [52, 55, 61, 544, 1764, 2204, 2461, 2463, 2656, 2658],\n+ \"56\": [52, 55, 61, 544, 1764, 2204, 2463, 2656, 2658],\n \"5612\": 2621,\n \"5614\": 2522,\n \"562\": [680, 2658],\n \"5620499351813308\": 86,\n \"5625\": 2491,\n \"56294995342131\": 2083,\n \"5640\": [2353, 2400, 2450],\n+ \"56660927\": 2461,\n \"567\": 2643,\n \"56826729e\": 2104,\n \"56917101\": 2634,\n \"57\": [58, 669, 2204, 2322, 2366, 2413, 2463, 2491, 2636, 2656],\n \"5707963267948966\": [102, 125],\n \"57079633\": [94, 105, 130, 1911, 2238, 2665],\n \"5708\": [412, 618],\n@@ -35234,15 +35233,14 @@\n \"650\": 2618,\n \"6500\": 2522,\n \"6501\": 2522,\n \"65028784\": 2665,\n \"65143654\": 1154,\n \"6515\": [2353, 2400, 2450],\n \"65200189e\": 566,\n- \"65221405\": 2461,\n \"6526\": 2522,\n \"6527\": 2522,\n \"6530\": 2522,\n \"6532\": 2522,\n \"6536\": 2522,\n \"6537\": 2522,\n \"6538\": 2522,\n@@ -35301,15 +35299,15 @@\n \"6678\": 2522,\n \"6686\": 2522,\n \"6689502\": 2576,\n \"669\": 669,\n \"6695\": 2522,\n \"6697\": 2522,\n \"6698\": 2522,\n- \"67\": [409, 670, 671, 672, 1901, 2461, 2542, 2643, 2656, 2665],\n+ \"67\": [409, 670, 671, 672, 1901, 2542, 2643, 2656, 2665],\n \"67046769e\": 147,\n \"6717\": 2522,\n \"6718\": 2522,\n \"6719\": 2522,\n \"6721\": 2522,\n \"6726\": 2522,\n \"6735\": 2522,\n@@ -35318,14 +35316,15 @@\n \"6756\": 2522,\n \"6757\": 2522,\n \"6765\": 28,\n \"6771\": 2522,\n \"6775\": 2522,\n \"6780\": 2522,\n \"6781\": 2522,\n+ \"6782615\": 2461,\n \"6783\": 2522,\n \"6785\": 2522,\n \"68\": [2656, 2658, 2665],\n \"6805\": [2353, 2400, 2450],\n \"6807\": 2522,\n \"68080986\": 349,\n \"6813\": 2522,\n@@ -35333,18 +35332,19 @@\n \"6819\": 2522,\n \"68206631e\": 2104,\n \"684\": [2463, 2572],\n \"6840\": 2524,\n \"6843\": 2524,\n \"68456316\": [2339, 2352, 2382, 2389, 2399, 2429, 2436, 2449],\n \"68482974\": 1153,\n+ \"68786807\": 2461,\n \"6884\": 2524,\n \"68862757\": 660,\n \"6888893\": [2352, 2399, 2449],\n- \"69\": [58, 431, 2656, 2665],\n+ \"69\": [58, 431, 2461, 2656, 2665],\n \"6916\": 2524,\n \"6922\": 2524,\n \"6924\": 2524,\n \"69312169\": [1113, 1543],\n \"69314718\": [76, 657, 2654],\n \"69314718055994529\": 657,\n \"6931471805599453\": 2257,\n@@ -35353,15 +35353,14 @@\n \"6943\": 2524,\n \"6949\": 2524,\n \"6950\": 2524,\n \"6952\": 2524,\n \"69583040e\": [420, 947],\n \"69646919\": 1153,\n \"69736803\": [349, 2457, 2638],\n- \"698686\": 2461,\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, 1248, 1249, 1278, 1283, 1286, 1306, 1312, 1331, 1334, 1342, 1344, 1346, 1433, 1437, 1440, 1460, 1466, 1510, 1512, 1520, 1521, 1522, 1554, 1615, 1638, 1644, 1647, 1656, 1672, 1695, 1704, 1705, 1729, 1758, 1770, 1786, 1805, 1816, 1843, 1870, 1880, 1882, 1904, 1908, 1912, 1913, 1914, 1916, 1953, 1957, 1960, 1980, 1986, 2071, 2076, 2078, 2079, 2081, 2082, 2085, 2087, 2091, 2096, 2098, 2104, 2107, 2110, 2115, 2116, 2162, 2163, 2164, 2168, 2171, 2172, 2204, 2205, 2206, 2208, 2209, 2210, 2211, 2212, 2222, 2224, 2225, 2235, 2236, 2237, 2238, 2240, 2241, 2246, 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, 2634, 2636, 2637, 2638, 2640, 2641, 2643, 2644, 2646, 2648, 2655, 2656, 2657, 2659, 2665],\n@@ -35372,29 +35371,29 @@\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+ \"70966625\": 2461,\n \"71\": [354, 650, 2460, 2656],\n \"71080601\": 2658,\n \"71238898\": 1911,\n \"71387850e\": 1586,\n \"718281\": 431,\n \"71828182845904523536028747135266249775724709369995\": 76,\n \"71828183\": [38, 2665],\n \"718282\": 2641,\n \"7183\": 2641,\n \"7185\": [99, 906],\n \"71946897\": 1153,\n \"72\": [13, 355, 544, 669, 1764, 2463, 2572, 2656, 2658],\n \"720\": [55, 356, 358, 1897, 2225, 2238, 2576],\n \"72075441\": 680,\n- \"72167143\": 2461,\n \"721fc64\": 13,\n \"72375\": 1644,\n \"72538256\": [103, 126],\n \"72686684e\": 566,\n \"72717132\": 2658,\n \"72727273\": 136,\n \"72847407\": 1154,\n@@ -35527,25 +35526,26 @@\n \"801\": [941, 1114, 1123, 1124, 1131],\n \"8010\": 2527,\n \"8020\": 2527,\n \"8024\": 2527,\n \"8031\": 2527,\n \"804\": 2508,\n \"8044\": 2527,\n+ \"80481925\": 2461,\n \"8058837395885292\": 666,\n \"80b3a34\": 2614,\n \"81\": [1650, 1884, 2634, 2640, 2644, 2656, 2665],\n \"81299683\": 2634,\n \"812997\": 2634,\n \"813\": [270, 880, 1069, 1229, 1312, 1466, 1986],\n \"81327024\": 2634,\n \"81349206\": [1113, 1543],\n \"81814867\": [2339, 2352, 2382, 2389, 2399, 2429, 2436, 2449],\n \"8192\": [72, 517, 2092, 2619],\n- \"82\": [1650, 2323, 2367, 2414, 2463, 2656, 2665],\n+ \"82\": [1650, 2323, 2367, 2414, 2461, 2463, 2656, 2665],\n \"8207540608310198\": [2353, 2400, 2450],\n \"82276161\": 349,\n \"8230\": [2353, 2400, 2450],\n \"82485143\": 2634,\n \"82502011\": 349,\n \"8255\": 2566,\n \"826716f\": 2521,\n@@ -35558,14 +35558,15 @@\n \"83314899\": 1154,\n \"83333333\": 1702,\n \"833333333333333\": [893, 1083, 1143, 2240],\n \"8341\": 2528,\n \"8346\": 2528,\n \"83571711\": 349,\n \"83697020e\": [470, 1899, 1900],\n+ \"8387832\": 2461,\n \"84\": [2656, 2658],\n \"840\": 1212,\n \"84057254\": [2339, 2352, 2382, 2389, 2399, 2429, 2436, 2449],\n \"84090247\": 2458,\n \"84123594\": 523,\n \"84147098\": 2665,\n \"8414709848078965\": 2639,\n@@ -35592,14 +35593,15 @@\n \"86399\": 55,\n \"86400\": 55,\n \"86401\": 55,\n \"8660254\": 2103,\n \"86820401\": [2345, 2391, 2439],\n \"86864911e\": 1586,\n \"87\": [2616, 2656],\n+ \"87332896\": 2488,\n \"875\": [478, 2491],\n \"8755\": [186, 827, 999, 1172, 1259, 1414, 1933],\n \"87649168120691\": 674,\n \"8770\": [2353, 2400, 2450],\n \"88\": [408, 2462, 2463, 2656, 2658, 2667],\n \"8801\": [99, 906],\n \"88031624\": 2665,\n@@ -35616,30 +35618,28 @@\n \"8900451\": 1154,\n \"89086505\": [2352, 2399, 2449],\n \"89206682e\": 2104,\n \"8922078\": 2458,\n \"89442719\": 642,\n \"89442719j\": 642,\n \"89721355\": 349,\n- \"89725564\": 2461,\n \"89804309e\": 2104,\n \"89920014\": [2319, 2363, 2410],\n \"8999999999999999\": 2107,\n \"8b2\": 2554,\n \"8b3\": 2555,\n \"8b4\": 2556,\n \"8d\": 11,\n \"8e\": [533, 669],\n \"8f\": [386, 406],\n \"8j\": [2101, 2241],\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, 543, 548, 565, 566, 573, 577, 608, 640, 641, 642, 644, 646, 648, 653, 655, 656, 659, 660, 661, 664, 666, 669, 680, 823, 830, 838, 839, 853, 860, 863, 864, 865, 880, 881, 886, 887, 888, 893, 896, 903, 904, 905, 908, 912, 913, 914, 919, 920, 921, 924, 926, 927, 936, 939, 947, 950, 952, 953, 957, 963, 993, 1002, 1010, 1013, 1033, 1044, 1048, 1049, 1050, 1060, 1069, 1070, 1076, 1077, 1078, 1083, 1104, 1106, 1107, 1108, 1113, 1116, 1119, 1135, 1142, 1143, 1145, 1148, 1149, 1157, 1159, 1160, 1161, 1164, 1166, 1167, 1184, 1193, 1194, 1195, 1200, 1204, 1205, 1206, 1212, 1213, 1223, 1228, 1229, 1236, 1240, 1241, 1246, 1247, 1249, 1271, 1283, 1306, 1312, 1324, 1334, 1335, 1342, 1348, 1426, 1437, 1460, 1466, 1478, 1483, 1510, 1512, 1521, 1527, 1540, 1543, 1545, 1586, 1644, 1650, 1656, 1707, 1752, 1762, 1808, 1816, 1870, 1876, 1882, 1884, 1885, 1886, 1903, 1904, 1907, 1908, 1912, 1913, 1914, 1916, 1945, 1957, 1980, 1986, 1998, 2079, 2085, 2087, 2091, 2104, 2107, 2110, 2111, 2115, 2116, 2118, 2128, 2134, 2140, 2148, 2149, 2150, 2161, 2168, 2171, 2204, 2205, 2206, 2208, 2209, 2210, 2211, 2223, 2224, 2225, 2236, 2237, 2238, 2239, 2240, 2246, 2248, 2257, 2303, 2316, 2319, 2327, 2328, 2332, 2334, 2341, 2342, 2347, 2361, 2363, 2376, 2384, 2388, 2395, 2408, 2410, 2423, 2431, 2435, 2445, 2457, 2461, 2463, 2488, 2489, 2491, 2508, 2513, 2519, 2520, 2521, 2522, 2525, 2566, 2567, 2568, 2569, 2570, 2571, 2572, 2576, 2577, 2578, 2580, 2583, 2586, 2587, 2590, 2592, 2599, 2600, 2601, 2602, 2603, 2604, 2605, 2606, 2616, 2622, 2623, 2624, 2625, 2630, 2632, 2634, 2637, 2638, 2640, 2643, 2644, 2646, 2647, 2648, 2656, 2657, 2664, 2665, 2667],\n \"90\": [25, 29, 33, 37, 39, 55, 68, 78, 363, 1910, 2082, 2103, 2248, 2463, 2610, 2653, 2656],\n \"90384387e\": 2104,\n \"90476190e\": 1816,\n- \"90602207\": 2461,\n \"90909091\": 136,\n \"909297\": 2641,\n \"90929743\": 2665,\n \"91\": 2656,\n \"91275558\": 2634,\n \"916666666666666\": 1240,\n \"92\": [98, 2656, 2658],\n@@ -35679,14 +35679,15 @@\n \"9378\": 2532,\n \"9379\": 2532,\n \"9390\": [2533, 2534],\n \"94\": [409, 669, 2634, 2656],\n \"940\": 2587,\n \"941257\": 2634,\n \"94125714\": 2634,\n+ \"94319463\": 2488,\n \"94708397920832\": 2641,\n \"9475673279178444\": 2348,\n \"94864945\": 2665,\n \"94909878\": [2387, 2434],\n \"95\": [37, 39, 646, 2353, 2400, 2450, 2634, 2653, 2656],\n \"9504637\": 2665,\n \"950684\": 2634,\n"}]}]}]}]}]}