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-20 ms +- 537 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-45.4 ms +- 1.08 ms per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+1.37 ms +- 57.6 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+2.63 ms +- 24.7 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-12 ms +- 380 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-27.9 ms +- 2.01 ms per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+725 us +- 5.67 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+1.94 ms +- 13.9 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-6.52 ms +- 188 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-12.1 ms +- 528 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+2.67 ms +- 10.9 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+5.06 ms +- 14.5 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([0.61364353, 0.63834349, 0.22803551])\n+Out[7]: array([0.87262273, 0.47345332, 0.75515287])\n \n In [8]: rng.random(3, dtype=np.float32)\n-Out[8]: array([0.07393819, 0.24147004, 0.89591014], dtype=float32)\n+Out[8]: array([0.79836625, 0.9985497 , 0.73898697], dtype=float32)\n \n In [9]: rng.integers(0, 256, size=3, dtype=np.uint8)\n-Out[9]: array([ 65, 24, 184], dtype=uint8)\n+Out[9]: array([122, 29, 52], 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([0.95099952, 0.32056607])\n+Out[12]: array([0.32027157, 0.04566187])\n \n In [13]: print(existing)\n-[0.95099952 0.32056607 0. 0. ]\n+[0.32027157 0.04566187 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([0.80843224, 0.61860788])\n+Out[4]: array([0.99519839, 0.45271714])\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([4.25655296, 3.63794509], domain=[0., 9.], window=[-1., 1.], symbol='x')\n+Out[6]: Polynomial([4.93110991, 4.47839277], 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([0.61860788, 0.80843224], domain=[-1., 1.], window=[-1., 1.], symbol='x')\n+Out[7]: Polynomial([0.45271714, 0.99519839], 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([0.80843224, 0.61860788])\n+Out[4]: array([0.99519839, 0.45271714])\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([4.25655296, 3.63794509], domain=[0., 9.], window=[-1.,\n+Out[6]: Polynomial([4.93110991, 4.47839277], 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([0.61860788, 0.80843224], domain=[-1., 1.], window=[-1.,\n+Out[7]: Polynomial([0.45271714, 0.99519839], 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": "@@ -32337,15 +32337,15 @@\n \"00578369\": 1754,\n \"00625\": 1585,\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, 2461, 2525, 2658],\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 \"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@@ -32383,38 +32383,38 @@\n \"03t13\": 55,\n \"04\": [54, 55, 164, 410, 547, 1586, 2463, 2594, 2659],\n \"0400\": 360,\n \"04097352\": 2635,\n \"04166667\": [1544, 1585],\n \"04211c6\": 2521,\n \"04551152e\": 2104,\n+ \"04566187\": 2461,\n \"04719755\": 1911,\n \"05\": [55, 91, 163, 410, 548, 669, 896, 1095, 1871, 2083, 2173, 2353, 2400, 2450, 2648],\n \"0500\": 360,\n \"05093587\": 2635,\n \"05208333\": 1585,\n \"05263157894736836\": 2257,\n \"0549999999999997\": 2083,\n \"055\": 2083,\n \"0596779\": 1153,\n- \"06\": [55, 566, 2083, 2508],\n+ \"06\": [55, 566, 2083, 2461, 2508],\n \"0614962j\": [439, 453],\n \"0625\": [418, 624, 1645],\n \"06369197489564249\": 2458,\n \"06381726\": 349,\n \"0660\": [302, 2131],\n \"06959433e\": [420, 947],\n \"07\": [55, 164, 547, 896, 897, 1335, 2170, 2508],\n \"07106781e\": 514,\n- \"07393819\": 2461,\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, 2461, 2525, 2659],\n+ \"08\": [55, 91, 147, 410, 523, 548, 896, 1095, 2322, 2366, 2413, 2525, 2659],\n \"0800\": 2525,\n \"08187135\": 54,\n \"08333333\": [1645, 1871],\n \"08405657\": 1867,\n \"0855\": 2642,\n \"08553692\": 38,\n \"085537\": 2642,\n@@ -32687,15 +32687,15 @@\n \"12150\": 2625,\n \"12187\": 2545,\n \"12188\": 2545,\n \"12189\": 2545,\n \"12190\": 2545,\n \"12191\": 2545,\n \"12192\": 2545,\n- \"122\": [431, 2463],\n+ \"122\": [431, 2461, 2463],\n \"12223\": 2098,\n \"12224\": 2098,\n \"12237\": 2545,\n \"12238\": 2545,\n \"122807528840384100672342137672332424406\": 2458,\n \"12284\": 2560,\n \"12296\": 2546,\n@@ -33285,15 +33285,15 @@\n \"18354\": 2573,\n \"18356\": 2573,\n \"18357\": 2573,\n \"18359\": 2573,\n \"1837\": 2611,\n \"1838\": 2611,\n \"18382\": 2574,\n- \"184\": [520, 2461, 2572],\n+ \"184\": [520, 2572],\n \"1843\": 2611,\n \"18459\": 2574,\n \"18460\": 2574,\n \"18461\": 2574,\n \"18462\": 2574,\n \"18469\": 2574,\n \"1848\": 2612,\n@@ -33333,15 +33333,15 @@\n \"1874\": 2611,\n \"1875\": 1585,\n \"18763\": 2575,\n \"18764\": 2575,\n \"18768\": 2575,\n \"18769\": 2575,\n \"18794\": 2575,\n- \"188\": [2461, 2463, 2637],\n+ \"188\": [2463, 2637],\n \"1885\": 2611,\n \"18874\": 2576,\n \"1887902\": 1911,\n \"18880\": 2576,\n \"18884\": 2583,\n \"18887\": 2575,\n \"189\": 2327,\n@@ -33514,15 +33514,15 @@\n \"1l_0\": 1822,\n \"1rc1\": 577,\n \"1st\": [36, 74, 642, 2616, 2637, 2641],\n \"1th\": [661, 2168],\n \"1type\": 2554,\n 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2571, 2576, 2577, 2583, 2584, 2594, 2599, 2602, 2603, 2608, 2622, 2627, 2635, 2637, 2641, 2642, 2645, 2657, 2658, 2666],\n \"200\": [441, 446, 2337, 2339, 2346, 2354, 2357, 2380, 2382, 2392, 2401, 2404, 2427, 2429, 2441, 2451, 2454, 2645, 2648, 2666],\n \"2000\": [514, 526, 2525, 2613],\n \"20000\": [2316, 2359, 2361, 2406, 2408, 2456, 2583],\n \"2000000\": 2635,\n \"20000000e\": 897,\n \"2001\": [55, 2322, 2326, 2329, 2330, 2331, 2335, 2339, 2340, 2366, 2371, 2373, 2374, 2375, 2378, 2382, 2383, 2413, 2418, 2420, 2421, 2422, 2425, 2429, 2430],\n \"2002\": [55, 360, 2316, 2323, 2353, 2361, 2367, 2400, 2408, 2414, 2450],\n@@ -33860,15 +33860,14 @@\n \"22733602246716966\": 2457,\n \"22740995\": 1149,\n \"22769\": 2599,\n \"22776\": 2599,\n \"22776602\": [680, 2659],\n \"22786\": 2599,\n \"228\": 2463,\n- \"22803551\": 2461,\n \"22820\": 2595,\n \"22830\": 2595,\n \"22831\": 2595,\n \"22832\": 2595,\n \"22834\": 2595,\n \"22837\": 2595,\n \"22839\": 2595,\n@@ -34017,15 +34016,14 @@\n \"24122\": 2600,\n \"24126\": 2622,\n \"24127\": 2600,\n \"24128\": 2600,\n \"24129\": 2600,\n \"24134\": 2600,\n \"24144\": 2622,\n- \"24147004\": 2461,\n \"24148\": 2601,\n \"24154\": 2622,\n \"24174\": 2601,\n \"24179\": 2601,\n \"24182\": 2601,\n \"24183\": 2601,\n \"24184\": 2601,\n@@ -34298,15 +34296,14 @@\n \"25618\": 2606,\n \"25619\": 2606,\n \"25620\": 2606,\n \"25630\": 2606,\n \"25643\": 2606,\n \"25645\": 2606,\n \"25651\": 2622,\n- \"25655296\": 2488,\n \"25658\": 2606,\n \"25663706\": 1891,\n \"25670\": 2606,\n \"25675\": 2629,\n \"25693945\": 2458,\n \"256x256x3\": 2637,\n \"257\": 2613,\n@@ -34396,15 +34393,15 @@\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@@ -34599,15 +34596,15 @@\n \"28657\": 28,\n \"28790332\": 2666,\n \"2883\": [1643, 1655],\n \"28853036\": 1867,\n \"28904982231052\": 675,\n \"2892\": 2615,\n \"28mathematical_const\": 76,\n- \"29\": [10, 21, 45, 54, 55, 76, 144, 163, 1638, 1647, 2208, 2328, 2463, 2464, 2513, 2547, 2548, 2549, 2550, 2551, 2552, 2553, 2554, 2555, 2556, 2557, 2558, 2559, 2560, 2561, 2562, 2563, 2564, 2565, 2566, 2567, 2568, 2587, 2602, 2622, 2641, 2657, 2666],\n+ \"29\": [10, 21, 45, 54, 55, 76, 144, 163, 1638, 1647, 2208, 2328, 2461, 2463, 2464, 2513, 2547, 2548, 2549, 2550, 2551, 2552, 2553, 2554, 2555, 2556, 2557, 2558, 2559, 2560, 2561, 2562, 2563, 2564, 2565, 2566, 2567, 2568, 2587, 2602, 2622, 2641, 2657, 2666],\n \"290\": 2300,\n \"29001ed\": 13,\n \"290301\": 55,\n \"292\": 55,\n \"29229249\": 524,\n \"29239766\": 54,\n \"2925464970228\": 657,\n@@ -34706,15 +34703,15 @@\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, 2633, 2637, 2639, 2641, 2645, 2646, 2648, 2649, 2652, 2657, 2658, 2659, 2666],\n \"320\": 1149,\n \"32000\": 2094,\n- \"32056607\": 2461,\n+ \"32027157\": 2461,\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@@ -34778,30 +34775,30 @@\n \"3628523\": 2458,\n \"36363636\": 136,\n \"3644j\": [415, 621],\n \"365\": [544, 1344, 1346, 1522, 1908],\n \"366\": 55,\n \"36674\": 2098,\n \"36787944\": [1660, 1774],\n- \"37\": [59, 60, 136, 1913, 2083, 2204, 2236, 2463, 2641, 2657, 2666],\n+ \"37\": [59, 60, 136, 1913, 2083, 2204, 2236, 2461, 2463, 2641, 2657, 2666],\n \"370\": 652,\n \"3701\": 2615,\n \"37079802\": [349, 2639],\n \"3712\": 2615,\n \"3728\": 2615,\n \"3728973198\": 2594,\n \"3743\": 2615,\n \"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, 2510, 2572, 2657, 2666],\n- \"380\": [2238, 2461, 2576],\n+ \"380\": [2238, 2576],\n \"38268343\": 642,\n \"38268343j\": 642,\n \"3832\": 2615,\n \"38434191e\": 660,\n \"38446749\": 1867,\n \"385\": [2270, 2300],\n \"3854\": [287, 1241, 1324, 1478, 1998],\n@@ -34939,21 +34936,22 @@\n \"4476\": 2621,\n \"4483\": 2617,\n \"4485\": 2617,\n \"4486\": 2617,\n \"449294e\": 2170,\n \"44948974\": 2659,\n \"44999999925494177\": 2115,\n- \"45\": [12, 18, 38, 58, 94, 105, 130, 339, 666, 851, 866, 944, 1025, 1026, 1031, 1051, 1212, 1882, 1886, 2103, 2204, 2461, 2637, 2644, 2657, 2666],\n+ \"45\": [12, 18, 38, 58, 94, 105, 130, 339, 666, 851, 866, 944, 1025, 1026, 1031, 1051, 1212, 1882, 1886, 2103, 2204, 2637, 2644, 2657, 2666],\n \"450\": 55,\n \"45000005\": 2115,\n \"45038594\": [349, 2639],\n \"45053314\": 2635,\n \"4511316\": 2666,\n \"4520525295346629\": 1228,\n+ \"45271714\": 2488,\n \"4532\": [409, 661, 2168],\n \"4545724517479104\": 2460,\n \"45560727e\": 54,\n \"456\": 1921,\n \"4567\": 2644,\n \"45674898e\": 566,\n \"45a3d84\": 2521,\n@@ -34984,18 +34982,20 @@\n \"47108547995356098\": [2345, 2391, 2439],\n \"47140452j\": 2491,\n \"472\": 55,\n \"4722\": 2618,\n \"4723\": 2621,\n \"4730\": [409, 661, 2168],\n \"4733\": 2618,\n+ \"47345332\": 2461,\n \"47458546\": 349,\n \"47536961\": 349,\n \"47613949\": [2335, 2378, 2425],\n \"4774\": 2618,\n+ \"47839277\": 2488,\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, 2657, 2659],\n \"480\": [238, 858, 1041, 1207, 1290, 1444, 1964],\n \"4800\": 57,\n \"48000000\": 2635,\n \"4809319\": 1153,\n@@ -35087,26 +35087,24 @@\n \"52359878\": 1911,\n \"52380952e\": 1816,\n \"5240\": 2620,\n \"5251\": 2620,\n \"526\": 2463,\n \"5260\": [2353, 2400, 2450],\n \"5271\": 42,\n- \"528\": 2461,\n \"53\": [162, 457, 1638, 2208, 2551, 2554, 2657, 2666],\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 \"53657292\": 2666,\n \"536870910\": 1902,\n- \"537\": 2461,\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@@ -35148,15 +35146,15 @@\n \"5620499351813308\": 86,\n \"5625\": 2491,\n \"56294995342131\": 2083,\n \"5640\": [2353, 2400, 2450],\n \"567\": 2644,\n \"56826729e\": 2104,\n \"56917101\": 2635,\n- \"57\": [58, 669, 2204, 2322, 2366, 2413, 2463, 2491, 2637, 2657],\n+ \"57\": [58, 669, 2204, 2322, 2366, 2413, 2461, 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 \"57510612\": 660,\n \"576\": 2615,\n@@ -35202,45 +35200,41 @@\n \"60860684e\": 1594,\n \"609\": 2583,\n \"6094\": 2522,\n \"60x\": 2599,\n \"61\": [13, 2657],\n \"610\": 28,\n \"61119\": 2098,\n- \"61364353\": 2461,\n \"614064523559687\": 2115,\n \"6143849206349179\": [1113, 1543],\n \"6176\": [99, 906],\n \"61799388\": 1911,\n \"618\": 669,\n \"6180\": [2353, 2400, 2450],\n- \"61860788\": 2488,\n \"61988120985\": [2323, 2367, 2414],\n \"61c54bbd\": 42,\n \"62\": [542, 968, 969, 2323, 2333, 2367, 2377, 2414, 2424, 2657],\n \"6208\": 2522,\n \"6227766\": 514,\n \"623\": [2394, 2444],\n \"62318272\": [2319, 2363, 2410],\n \"62341325\": 514,\n \"62374854\": 2666,\n \"624\": [2300, 2370, 2394, 2417, 2444, 2462],\n \"625\": [99, 478, 645, 906, 2390, 2438],\n \"6273591314603949\": [2335, 2378, 2425],\n \"62949953e\": 645,\n- \"63\": [58, 514, 669, 1748, 1777, 2336, 2463, 2520, 2566, 2594, 2642, 2657],\n+ \"63\": [58, 514, 669, 1748, 1777, 2336, 2461, 2463, 2520, 2566, 2594, 2642, 2657],\n \"631198583\": 55,\n \"631198588\": 55,\n \"63317787e\": [2166, 2167],\n \"63526532\": 2458,\n \"636363636364\": [2353, 2400, 2450],\n \"63696169\": 2635,\n \"6376\": 2522,\n- \"63794509\": 2488,\n- \"63834349\": 2461,\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@@ -35259,15 +35253,15 @@\n \"6488\": 2522,\n \"6491\": 2522,\n \"6495\": 2522,\n \"6497\": 2522,\n \"6498\": 2522,\n \"6499\": 2522,\n \"64bit\": [50, 61, 62, 2364, 2377, 2379, 2388, 2411, 2424, 2426, 2435, 2517, 2572, 2594],\n- \"65\": [2461, 2657],\n+ \"65\": 2657,\n \"650\": 2618,\n \"6500\": 2522,\n \"6501\": 2522,\n \"65028784\": 2666,\n \"65143654\": 1154,\n \"6515\": [2353, 2400, 2450],\n \"65200189e\": 566,\n@@ -35333,15 +35327,15 @@\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, 2542, 2644, 2657, 2666],\n+ \"67\": [409, 670, 671, 672, 1901, 2461, 2542, 2644, 2657, 2666],\n \"67046769e\": 147,\n \"6717\": 2522,\n \"6718\": 2522,\n \"6719\": 2522,\n \"6721\": 2522,\n \"6726\": 2522,\n \"6735\": 2522,\n@@ -35419,28 +35413,30 @@\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 \"72949656\": 2635,\n \"73\": [2463, 2657],\n \"7320508075688772j\": 59,\n \"73472348e\": 1816,\n \"73496154e\": 1867,\n \"73603959e\": 2666,\n \"73799541\": 1153,\n+ \"73898697\": 2461,\n \"74\": [2463, 2513, 2514, 2657],\n \"74000000\": 2635,\n \"7416573867739413\": 653,\n \"74165739\": 653,\n \"74499359e\": [420, 947],\n \"745966692414834\": [648, 653],\n \"75\": [58, 135, 440, 478, 516, 520, 528, 544, 645, 667, 870, 1056, 1542, 1606, 1634, 1663, 1834, 2091, 2257, 2491, 2657, 2659, 2666],\n@@ -35455,14 +35451,15 @@\n \"7515\": [2353, 2400, 2450],\n \"75224494\": [2345, 2391, 2439],\n \"7530\": 2526,\n \"7535\": 2526,\n \"75351311\": 2666,\n \"754\": [62, 65, 69, 76, 457, 552, 555, 556, 558, 559, 1335, 1340, 1343, 2083, 2094, 2610, 2655],\n \"7551\": 2526,\n+ \"75515287\": 2461,\n \"7558\": 2526,\n \"756802\": 2642,\n \"7568025\": 2666,\n \"75682846\": 2659,\n \"7578\": 2526,\n \"7590\": 2526,\n \"75958653\": 1911,\n@@ -35539,14 +35536,15 @@\n \"7954\": 2527,\n \"7955\": 2527,\n \"79579319e\": 1867,\n \"79694221e\": 1586,\n \"7972\": 2527,\n \"7976931348623157e\": 1335,\n \"79769313e\": 1335,\n+ \"79836625\": 2461,\n \"79ff\": [102, 125],\n \"7e\": 669,\n \"7e13\": 55,\n \"7e17\": 55,\n \"7x\": [2566, 2599],\n \"8\": [9, 11, 13, 17, 18, 24, 26, 28, 30, 31, 32, 34, 36, 38, 39, 43, 47, 50, 56, 57, 58, 59, 60, 61, 62, 69, 72, 73, 74, 76, 89, 91, 96, 97, 98, 99, 114, 117, 118, 119, 132, 135, 141, 142, 149, 150, 169, 171, 172, 173, 209, 215, 229, 234, 261, 262, 270, 295, 313, 315, 320, 331, 332, 334, 337, 348, 355, 364, 365, 366, 367, 369, 370, 375, 385, 387, 391, 396, 399, 401, 406, 409, 410, 416, 417, 432, 435, 438, 440, 454, 455, 467, 470, 478, 486, 514, 520, 529, 530, 533, 538, 541, 543, 544, 546, 548, 554, 565, 566, 577, 608, 622, 623, 639, 640, 645, 651, 653, 656, 657, 659, 660, 661, 662, 664, 665, 666, 667, 680, 830, 854, 860, 863, 864, 865, 873, 880, 881, 883, 886, 887, 888, 893, 896, 903, 904, 905, 906, 912, 913, 914, 917, 919, 920, 921, 924, 926, 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2157, 2159, 2164, 2168, 2172, 2200, 2202, 2204, 2205, 2206, 2208, 2209, 2210, 2223, 2224, 2225, 2236, 2237, 2238, 2239, 2240, 2242, 2246, 2248, 2256, 2257, 2290, 2308, 2312, 2313, 2320, 2328, 2329, 2334, 2335, 2341, 2342, 2347, 2354, 2373, 2378, 2384, 2388, 2390, 2394, 2395, 2401, 2420, 2425, 2431, 2435, 2438, 2444, 2445, 2451, 2457, 2458, 2460, 2461, 2463, 2470, 2508, 2513, 2519, 2525, 2535, 2538, 2542, 2544, 2545, 2547, 2554, 2555, 2556, 2557, 2558, 2559, 2560, 2561, 2562, 2563, 2564, 2565, 2566, 2567, 2568, 2569, 2571, 2572, 2573, 2576, 2579, 2580, 2583, 2584, 2585, 2586, 2587, 2589, 2590, 2591, 2592, 2593, 2594, 2595, 2596, 2597, 2598, 2599, 2613, 2615, 2619, 2622, 2623, 2631, 2635, 2637, 2638, 2639, 2641, 2642, 2644, 2645, 2646, 2648, 2649, 2653, 2655, 2657, 2658, 2659, 2660, 2665, 2666],\n \"80\": [69, 396, 409, 446, 977, 2248, 2346, 2357, 2383, 2392, 2404, 2430, 2441, 2454, 2588, 2622, 2648, 2649, 2657],\n@@ -35558,15 +35556,14 @@\n \"8010\": 2527,\n \"8020\": 2527,\n \"8024\": 2527,\n \"8031\": 2527,\n \"804\": 2508,\n \"8044\": 2527,\n \"8058837395885292\": 666,\n- \"80843224\": 2488,\n \"80b3a34\": 2614,\n \"81\": [1650, 1884, 2635, 2641, 2645, 2657, 2666],\n \"81299683\": 2635,\n \"812997\": 2635,\n \"813\": [270, 880, 1069, 1229, 1312, 1466, 1986],\n \"81327024\": 2635,\n \"81349206\": [1113, 1543],\n@@ -35623,14 +35620,15 @@\n \"86399\": 55,\n \"86400\": 55,\n \"86401\": 55,\n \"8660254\": 2103,\n \"86820401\": [2345, 2391, 2439],\n \"86864911e\": 1586,\n \"87\": [2616, 2657],\n+ \"87262273\": 2461,\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, 2657, 2659, 2668],\n \"8801\": [99, 906],\n \"88031624\": 2666,\n@@ -35646,15 +35644,14 @@\n \"890\": 2644,\n \"8900451\": 1154,\n \"89086505\": [2352, 2399, 2449],\n \"89206682e\": 2104,\n \"8922078\": 2458,\n \"89442719\": 642,\n \"89442719j\": 642,\n- \"89591014\": 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@@ -35689,14 +35686,15 @@\n \"92676499\": [349, 2639],\n \"927\": [539, 554],\n \"92771843\": 1154,\n \"9299\": 2532,\n \"93\": 2657,\n \"9304e\": 2091,\n \"931\": 2587,\n+ \"93110991\": 2488,\n \"9317\": 2532,\n \"9319\": 2532,\n \"9339\": 2532,\n \"9340\": 2532,\n \"934284\": 349,\n \"93657855\": 349,\n \"9371\": 2532,\n@@ -35705,27 +35703,26 @@\n \"9374\": 2532,\n \"9376\": 2532,\n \"9377\": 2532,\n \"93773029\": 349,\n \"9378\": 2532,\n \"9379\": 2532,\n \"9390\": [2533, 2534],\n- \"94\": [409, 669, 2635, 2657],\n+ \"94\": [409, 669, 2461, 2635, 2657],\n \"940\": 2587,\n \"941257\": 2635,\n \"94125714\": 2635,\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 \"95068423\": 2635,\n- \"95099952\": 2461,\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@@ -35793,18 +35790,20 @@\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+ \"99519839\": 2488,\n \"99734545\": 1154,\n \"998\": 2535,\n \"99822295\": [103, 126],\n \"99827656\": 1754,\n+ \"9985497\": 2461,\n \"99885316e\": 566,\n \"999\": [543, 844, 864, 887, 1020, 1049, 1077, 1125, 2535, 2644],\n \"9990000e\": 1335,\n \"99923895\": 349,\n \"9997\": 2666,\n \"99978457\": 1697,\n \"9998\": 2666,\n"}]}]}]}]}]}