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-1.39 ms +- 52.3 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-2.55 ms +- 334 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+1.48 ms +- 31.1 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+2.85 ms +- 16.6 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-651 us +- 126 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-1.44 ms +- 108 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+701 us +- 19.7 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+2.04 ms +- 27.8 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-3.15 ms +- 175 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-4.58 ms +- 277 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+2.85 ms +- 53.4 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+6.54 ms +- 975 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([0.70547514, 0.08925294, 0.40291075])\n+Out[7]: array([0.1171073 , 0.60991664, 0.51373836])\n \n In [8]: rng.random(3, dtype=np.float32)\n-Out[8]: array([0.7055436 , 0.81983244, 0.7707724 ], dtype=float32)\n+Out[8]: array([0.14971465, 0.04142678, 0.91847485], dtype=float32)\n \n In [9]: rng.integers(0, 256, size=3, dtype=np.uint8)\n-Out[9]: array([ 48, 53, 194], dtype=uint8)\n+Out[9]: array([198, 105, 169], 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([0.83725004, 0.59525983])\n+Out[12]: array([0.46374678, 0.08005731])\n \n In [13]: print(existing)\n-[0.83725004 0.59525983 0. 0. ]\n+[0.46374678 0.08005731 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.
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([ 1.11425062, -0.49272213])\n+Out[4]: array([0.95430353, 0.03065741])\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([4.52140567, 5.0141278 ], domain=[0., 9.], window=[-1., 1.], symbol='x')\n+Out[6]: Polynomial([4.32502331, 4.2943659 ], 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([-0.49272213, 1.11425062], domain=[-1., 1.], window=[-1., 1.], symbol='x')\n+Out[7]: Polynomial([0.03065741, 0.95430353], 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([ 1.11425062, -0.49272213])\n+Out[4]: array([0.95430353, 0.03065741])\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([4.52140567, 5.0141278 ], domain=[0., 9.], window=[-1.,\n+Out[6]: Polynomial([4.32502331, 4.2943659 ], 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([-0.49272213, 1.11425062], domain=[-1., 1.], window=[-1.,\n+Out[7]: Polynomial([0.03065741, 0.95430353], 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": "@@ -32345,15 +32345,14 @@\n \"010\": [653, 1602, 1659, 1716, 1773, 1830, 1886],\n \"0100\": 1519,\n \"01041667\": 1585,\n \"011\": [1602, 1659, 1716, 1773, 1830, 1886],\n \"012\": [1602, 1659, 1716, 1773, 1830, 1886],\n \"0123456789\": [303, 2132],\n \"01280782\": [2335, 2378, 2425],\n- \"0141278\": 2488,\n \"016\": [648, 653],\n \"01652764\": 2635,\n \"01666667\": 1544,\n \"016j\": 2105,\n \"01831564\": 1660,\n \"018318\": [2353, 2400, 2450],\n \"01j\": 514,\n@@ -32370,25 +32369,27 @@\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+ \"03065741\": 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 \"03t13\": 55,\n- \"04\": [54, 55, 164, 410, 547, 1586, 2463, 2594, 2659],\n+ \"04\": [54, 55, 164, 410, 547, 1586, 2461, 2463, 2594, 2659],\n \"0400\": 360,\n \"04097352\": 2635,\n+ \"04142678\": 2461,\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, 2252, 2353, 2400, 2450, 2648],\n \"0500\": 360,\n \"05093587\": 2635,\n@@ -32408,25 +32409,25 @@\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 \"0800\": 2525,\n+ \"08005731\": 2461,\n \"08187135\": 54,\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- \"08925294\": 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@@ -32525,15 +32526,15 @@\n \"10403\": 2536,\n \"10412\": 2536,\n \"10424\": 2536,\n \"10425\": 2536,\n \"10431\": 2536,\n \"10435\": 2536,\n \"1049\": 2098,\n- \"105\": 2463,\n+ \"105\": [2461, 2463],\n \"10534\": 2536,\n \"10536\": 2536,\n \"10537\": 2536,\n \"10539\": 2536,\n \"10540\": 2536,\n \"10541\": 2536,\n \"10542\": 2536,\n@@ -32564,15 +32565,15 @@\n \"1071\": 2463,\n \"10725\": 2537,\n \"10726\": 2537,\n \"10727\": 2537,\n \"10729\": 2537,\n \"1073741821\": [420, 421, 947, 948, 1923],\n \"1078\": 2622,\n- \"108\": [524, 2461, 2463],\n+ \"108\": [524, 2463],\n \"10862\": 2538,\n \"10868\": 2538,\n \"1088311\": 2343,\n \"10898\": 2542,\n \"109\": [136, 523, 2463],\n \"10905\": 2538,\n \"10941\": 2328,\n@@ -32620,15 +32621,14 @@\n \"11294\": 2540,\n \"113\": [674, 2463, 2666],\n \"11308\": 2542,\n \"1138\": 2612,\n \"114\": 2463,\n \"11407192\": 1822,\n \"1142\": [2353, 2400, 2450],\n- \"11425062\": 2488,\n \"1149\": 2612,\n \"115\": [1654, 2463],\n \"1151\": 657,\n \"11525\": 2547,\n \"116\": 2463,\n \"11625\": [2543, 2544, 2545, 2546],\n \"11647\": 2543,\n@@ -32637,14 +32637,15 @@\n \"11659149\": [2345, 2391, 2439],\n \"11661\": 2543,\n \"11665\": 2543,\n \"11675684e\": 1586,\n \"11682\": 2543,\n \"11698\": 2543,\n \"11700\": 2543,\n+ \"1171073\": 2461,\n \"11719\": 2543,\n \"11720\": 2543,\n \"11746\": 2543,\n \"11757\": 2543,\n \"11758\": 2543,\n \"11759\": 2543,\n \"11760\": 2543,\n@@ -32722,15 +32723,15 @@\n \"1234567e\": 2172,\n \"12346\": 2462,\n \"1235\": 2091,\n \"123abc\": [302, 305, 2131, 2134],\n \"124\": [98, 905],\n \"125\": [470, 660, 1114, 1142, 1645, 1651, 1899, 1900, 2239, 2339, 2382, 2429, 2460, 2491, 2659, 2666],\n \"12589991e\": 645,\n- \"126\": [863, 1048, 1116, 1904, 2461],\n+ \"126\": [863, 1048, 1116, 1904],\n \"1261\": 2612,\n \"12658\": 2560,\n \"12697628\": 2635,\n \"127\": [62, 66, 514, 863, 1048, 1102, 1116, 1904, 2301, 2302, 2462, 2463, 2464, 2583, 2639],\n \"12736\": [2548, 2549],\n \"12767\": 2548,\n \"12768\": 2548,\n@@ -32967,14 +32968,15 @@\n \"1486618624\": 2648,\n \"14882\": 2572,\n \"14924\": 2566,\n \"14933\": 2566,\n \"14937\": 2559,\n \"14939\": 2559,\n \"14942\": 2566,\n+ \"14971465\": 2461,\n \"14981\": 2566,\n \"14987721\": 2666,\n \"14993\": 2559,\n \"14995\": 2566,\n \"14996\": 2560,\n \"14j\": 1915,\n \"14t15\": 55,\n@@ -33158,14 +33160,15 @@\n \"168\": 2463,\n \"16815\": 2572,\n \"16830\": 2588,\n \"16832\": 2567,\n \"16841\": 2572,\n \"16872\": 2567,\n \"16875\": 2567,\n+ \"169\": 2461,\n \"16904\": 2567,\n \"16905\": 2567,\n \"16906\": 2567,\n \"16916\": 2567,\n \"16922\": 2567,\n \"16938\": 2572,\n \"16959\": 2568,\n@@ -33211,15 +33214,15 @@\n \"174\": 2463,\n \"17446\": 2569,\n \"17450\": 2569,\n \"17456\": 2572,\n \"1747\": 2612,\n \"1749\": 2611,\n \"17492\": 2576,\n- \"175\": [2461, 2463, 2659],\n+ \"175\": [2463, 2659],\n \"17522\": 2569,\n \"17530\": 2583,\n \"17535\": 2572,\n \"17545176\": 1153,\n \"17568\": 2569,\n \"17577\": [2572, 2660],\n \"17580\": 2572,\n@@ -33406,15 +33409,14 @@\n \"19365\": 2577,\n \"19366\": 2577,\n \"19388\": 2594,\n \"1939\": [2356, 2358, 2403, 2405, 2453, 2455],\n \"19390\": 2577,\n \"19391\": 2577,\n \"19392\": 2577,\n- \"194\": 2461,\n \"1943\": [2332, 2376, 2423],\n \"19430\": 2577,\n \"19459\": 2583,\n \"19478\": 2583,\n \"19479\": 2583,\n \"1948\": 2612,\n \"19495\": 2577,\n@@ -33467,15 +33469,15 @@\n \"1971\": 55,\n \"1972\": [351, 2105, 2166, 2167, 2316, 2327, 2329, 2356, 2361, 2372, 2373, 2403, 2408, 2419, 2420, 2453],\n \"19745\": 2579,\n \"1975\": [136, 523, 524, 566],\n \"19754\": 2583,\n \"19775622\": 2642,\n \"1977562209304\": 2642,\n- \"198\": [36, 2666],\n+ \"198\": [36, 2461, 2666],\n \"1980\": [62, 637, 641, 642, 655, 658, 1526],\n \"19803\": 2583,\n \"19805\": 2583,\n \"1985\": [653, 1897],\n \"19857\": 2583,\n \"1986\": [136, 523, 524],\n \"19879\": 2583,\n@@ -34396,15 +34398,15 @@\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, 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, 2461, 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@@ -34483,15 +34485,14 @@\n \"27636\": [2628, 2629],\n \"27661\": 2629,\n \"27668\": 2628,\n \"27669\": 2628,\n \"27672\": 2628,\n \"27673\": 2628,\n \"27695\": 2629,\n- \"277\": 2461,\n \"27723\": 2629,\n \"27735\": 2629,\n \"27736\": 2629,\n \"27807\": 2629,\n \"27808\": 2629,\n \"27896\": 2629,\n \"278dd2a\": 13,\n@@ -34609,14 +34610,15 @@\n \"29001ed\": 13,\n \"290301\": 55,\n \"292\": 55,\n \"29229249\": 524,\n \"29239766\": 54,\n \"2925464970228\": 657,\n \"294241\": 55,\n+ \"2943659\": 2488,\n \"296\": 669,\n \"2969\": 2614,\n \"297\": [438, 2477, 2666],\n \"29718677\": [2339, 2352, 2382, 2389, 2399, 2429, 2436, 2449],\n \"2973\": 2614,\n \"29737120e\": 566,\n \"298\": [2300, 2666],\n@@ -34674,15 +34676,15 @@\n \"3057\": 2615,\n \"307\": [1149, 2666],\n \"308\": 1335,\n \"3083169284\": [850, 1030],\n \"308j\": 1335,\n \"309\": [420, 421, 947, 948, 1149, 2460],\n \"30z\": 360,\n- \"31\": [54, 55, 146, 336, 514, 669, 1088, 1094, 1638, 1711, 1867, 1913, 2204, 2236, 2327, 2331, 2375, 2422, 2513, 2520, 2637, 2641, 2657, 2666],\n+ \"31\": [54, 55, 146, 336, 514, 669, 1088, 1094, 1638, 1711, 1867, 1913, 2204, 2236, 2327, 2331, 2375, 2422, 2461, 2513, 2520, 2637, 2641, 2657, 2666],\n \"31018314\": 2458,\n \"3105\": 2614,\n \"3108\": 2614,\n \"3117\": 2614,\n \"3118\": [57, 2547],\n \"31183145\": 2666,\n \"312088\": 1867,\n@@ -34709,14 +34711,15 @@\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, 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+ \"32502331\": 2488,\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@@ -34731,15 +34734,14 @@\n \"33333333\": [1335, 1544, 1702, 1750, 1771, 1812, 1816, 1818, 1819, 1863, 1865, 2491, 2645],\n \"333333333\": 2171,\n \"3333333333333\": 2171,\n \"33333334\": 2171,\n \"3333333e\": 1335,\n \"33339\": 2173,\n \"33340274885464394\": 2202,\n- \"334\": 2461,\n \"3340\": [287, 1241, 1324, 1478, 1998],\n \"3348\": 2617,\n \"33486982e\": 438,\n \"3361\": [99, 906],\n \"3364\": 2615,\n \"3373\": 2615,\n \"33872321e\": 2104,\n@@ -34810,15 +34812,15 @@\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@@ -34850,15 +34852,14 @@\n \"4007\": 2620,\n \"40077\": [1644, 1656],\n \"400e\": 2658,\n \"4018\": [2615, 2617],\n \"4024\": 2617,\n \"4027\": 2617,\n \"40274501\": 1154,\n- \"40291075\": 2461,\n \"4051\": [2615, 2617],\n \"409\": 2463,\n \"40918587e\": 2104,\n \"40919914\": 2666,\n \"4093\": 2617,\n \"4094\": [2615, 2617],\n \"4096\": [72, 2092],\n@@ -34917,15 +34918,15 @@\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, 2461, 2463, 2624, 2657, 2658, 2659, 2666],\n+ \"44\": [16, 1525, 1758, 1905, 1907, 1922, 2208, 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@@ -34964,14 +34965,15 @@\n \"46009194e\": 566,\n \"4602\": 2618,\n \"4610935\": 457,\n \"4613\": 2618,\n \"4628\": 2618,\n \"46351241j\": 2081,\n \"46368\": 28,\n+ \"46374678\": 2461,\n \"464\": 680,\n \"4642\": 2618,\n \"465\": [58, 1157],\n \"4656\": 2618,\n \"4664\": [409, 661, 2168],\n \"46666491\": 349,\n \"46716228e\": 1586,\n@@ -35007,15 +35009,14 @@\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, 2641, 2657, 2666],\n- \"49272213\": 2488,\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@@ -35062,14 +35063,15 @@\n \"510\": [143, 570],\n \"5100\": 2620,\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+ \"51373836\": 2461,\n \"5138\": 2620,\n \"514229\": 28,\n \"5147\": 2620,\n \"5148\": 2620,\n \"51506735\": 1822,\n \"5155\": 2621,\n \"5162\": [409, 661, 2168],\n@@ -35078,17 +35080,16 @@\n \"51658839e\": 1586,\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, 2461, 2554, 2635, 2641, 2648, 2657, 2659, 2660, 2666],\n+ \"52\": [10, 50, 62, 457, 1638, 1647, 1650, 2204, 2208, 2554, 2635, 2641, 2648, 2657, 2659, 2660, 2666],\n \"5203\": 2620,\n- \"52140567\": 2488,\n \"5225\": 2620,\n \"5231\": 2620,\n \"52338984\": [2345, 2391, 2439],\n \"52359878\": 1911,\n \"52380952e\": 1816,\n \"5240\": 2620,\n \"5251\": 2620,\n@@ -35107,15 +35108,15 @@\n \"536870910\": 1902,\n \"5374\": 2621,\n \"53814331\": 2666,\n \"5388\": 2621,\n \"5390\": 2621,\n \"5393\": 2621,\n \"5396\": [287, 1241, 1324, 1478, 1998],\n- \"54\": [38, 59, 523, 1638, 1711, 1764, 2208, 2642, 2657],\n+ \"54\": [38, 59, 523, 1638, 1711, 1764, 2208, 2461, 2642, 2657],\n \"540\": [2238, 2576],\n \"54030231\": 2666,\n \"54030231j\": 2666,\n \"541\": 2463,\n \"54117\": 1644,\n \"5424\": 2621,\n \"54323428\": [2345, 2391, 2439],\n@@ -35126,15 +35127,15 @@\n \"5470\": [2353, 2400, 2450],\n \"5481\": 2621,\n \"5492\": 2621,\n \"54930614\": [106, 131],\n \"5493061443340549\": [413, 619],\n \"54959369\": 2666,\n \"54999924\": 1247,\n- \"55\": [28, 59, 60, 73, 893, 1083, 1143, 1525, 1905, 2090, 2204, 2240, 2461, 2622, 2657],\n+ \"55\": [28, 59, 60, 73, 893, 1083, 1143, 1525, 1905, 2090, 2204, 2240, 2622, 2657],\n \"55000000074505806\": 1247,\n \"5510652\": 2635,\n \"55111512e\": 642,\n \"55131477\": 1153,\n \"5524\": 2621,\n \"55458479\": 349,\n \"55490914e\": 2666,\n@@ -35164,24 +35165,23 @@\n \"576\": 2615,\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, 2461, 2464, 2572, 2635, 2657],\n+ \"58\": [669, 1748, 1777, 2204, 2208, 2332, 2376, 2423, 2464, 2572, 2635, 2657],\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- \"59525983\": 2461,\n \"595726\": 2635,\n \"59572603\": 2635,\n \"5969\": [99, 906],\n \"598150\": 2642,\n \"59815003\": 38,\n \"5982\": 2642,\n \"59903635e\": 147,\n@@ -35201,14 +35201,15 @@\n \"60393245\": 660,\n \"60546483\": 523,\n \"60663578\": 2635,\n \"607\": [2339, 2382, 2429],\n \"60860684e\": 1594,\n \"609\": 2583,\n \"6094\": 2522,\n+ \"60991664\": 2461,\n \"60x\": 2599,\n \"61\": [13, 2657],\n \"610\": 28,\n \"61119\": 2098,\n \"614064523559687\": 2115,\n \"6143849206349179\": [1113, 1543],\n \"6176\": [99, 906],\n@@ -35263,15 +35264,14 @@\n \"6499\": 2522,\n \"64bit\": [50, 61, 62, 2364, 2377, 2379, 2388, 2411, 2424, 2426, 2435, 2517, 2572, 2594],\n \"65\": 2657,\n \"650\": 2618,\n \"6500\": 2522,\n \"6501\": 2522,\n \"65028784\": 2666,\n- \"651\": 2461,\n \"65143654\": 1154,\n \"6515\": [2353, 2400, 2450],\n \"65200189e\": 566,\n \"6526\": 2522,\n \"6527\": 2522,\n \"6530\": 2522,\n \"6532\": 2522,\n@@ -35395,19 +35395,17 @@\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, 2635, 2637, 2638, 2639, 2641, 2642, 2644, 2645, 2647, 2649, 2656, 2657, 2658, 2660, 2666],\n \"70\": [59, 457, 567, 2241, 2248, 2657],\n \"700\": 567,\n \"70000000\": 2635,\n- \"701\": 2463,\n+ \"701\": [2461, 2463],\n \"703\": 2625,\n \"7054\": 2535,\n- \"70547514\": 2461,\n- \"7055436\": 2461,\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@@ -35487,15 +35485,14 @@\n \"7676\": 2526,\n \"7680\": 2526,\n \"769893\": 2635,\n \"76989341\": 2635,\n \"76991118\": 1891,\n \"77\": [29, 36, 37, 38, 39, 2463, 2635, 2654, 2657],\n \"770\": [287, 1241, 1324, 1478, 1998, 2650],\n- \"7707724\": 2461,\n \"77086955\": 1526,\n \"7724\": 2526,\n \"7725\": [2353, 2400, 2450],\n \"7731\": 2526,\n \"7736\": 2527,\n \"7737\": 2526,\n \"7738\": 2527,\n@@ -35570,15 +35567,14 @@\n \"81299683\": 2635,\n \"812997\": 2635,\n \"813\": [270, 880, 1069, 1229, 1312, 1466, 1986],\n \"81327024\": 2635,\n \"81349206\": [1113, 1543],\n \"81814867\": [2339, 2352, 2382, 2389, 2399, 2429, 2436, 2449],\n \"8192\": [72, 517, 2092, 2619],\n- \"81983244\": 2461,\n \"82\": [1650, 2323, 2367, 2414, 2463, 2657, 2666],\n \"8207540608310198\": [2353, 2400, 2450],\n \"82276161\": 349,\n \"8230\": [2353, 2400, 2450],\n \"82485143\": 2635,\n \"82502011\": 349,\n \"8255\": 2566,\n@@ -35592,28 +35588,27 @@\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- \"83725004\": 2461,\n \"84\": [2657, 2659],\n \"840\": 1212,\n \"84057254\": [2339, 2352, 2382, 2389, 2399, 2429, 2436, 2449],\n \"84090247\": 2458,\n \"84123594\": 523,\n \"84147098\": 2666,\n \"8414709848078965\": 2640,\n \"84147098j\": 2666,\n \"841471\": 2642,\n \"842523\": 2515,\n \"84680802e\": 2104,\n \"8480354764257312\": 653,\n- \"85\": [409, 2657],\n+ \"85\": [409, 2461, 2657],\n \"85099543\": 1822,\n \"85355339\": 1756,\n \"85569\": 2098,\n \"85602287\": [2335, 2378, 2425],\n \"857\": 410,\n \"8570331885190563e\": [648, 653],\n \"85715698e\": 2171,\n@@ -35671,14 +35666,15 @@\n \"90476190e\": 1816,\n \"90909091\": 136,\n \"909297\": 2642,\n \"90929743\": 2666,\n \"91\": 2657,\n \"91275558\": 2635,\n \"916666666666666\": 1240,\n+ \"91847485\": 2461,\n \"92\": [98, 2657, 2659],\n \"921fb54442d18p\": 2520,\n \"9223372036854775807\": 2648,\n \"9223372036854775808\": 2648,\n \"92346708\": 349,\n \"92362781e\": 2104,\n \"92387953\": 642,\n@@ -35720,14 +35716,15 @@\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 \"95068423\": 2635,\n+ \"95430353\": 2488,\n \"9555\": [2533, 2534],\n \"9556\": [2533, 2534],\n \"9557\": [2533, 2534],\n \"9558\": [2533, 2534],\n \"9559\": [2533, 2534],\n \"9580\": [2533, 2534],\n \"95892427\": 2666,\n@@ -35750,14 +35747,15 @@\n \"9732\": [2533, 2534],\n \"9736\": [2533, 2534],\n \"9742\": [2533, 2534],\n \"9744\": [2533, 2534],\n \"9745\": [2533, 2534],\n \"9746\": [2533, 2534],\n \"9747\": [2533, 2534],\n+ \"975\": 2461,\n \"97517215\": 349,\n \"97562235\": [349, 2457, 2639],\n \"9757\": [2533, 2534],\n \"9764\": [2533, 2534],\n \"9765\": [2533, 2534],\n \"9766\": [2533, 2534],\n \"9767\": [2533, 2534],\n"}]}]}]}]}]}