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-3.49 ms +- 721 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-7.84 ms +- 1.33 ms per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+1.36 ms +- 33.7 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+2.61 ms +- 17.5 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-1.93 ms +- 109 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-5.43 ms +- 1.18 ms per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+724 us +- 6.86 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+1.94 ms +- 10.5 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-8.56 ms +- 1.23 ms per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-13.7 ms +- 265 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+2.98 ms +- 21.3 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+5.05 ms +- 12.7 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([0.09837248, 0.04465839, 0.2084051 ])\n+Out[7]: array([0.55420097, 0.45697908, 0.69487323])\n \n In [8]: rng.random(3, dtype=np.float32)\n-Out[8]: array([0.13149399, 0.6899817 , 0.9949636 ], dtype=float32)\n+Out[8]: array([0.5988971 , 0.18808335, 0.86917627], dtype=float32)\n \n In [9]: rng.integers(0, 256, size=3, dtype=np.uint8)\n-Out[9]: array([119, 176, 212], dtype=uint8)\n+Out[9]: array([252, 61, 65], 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([0.55876893, 0.61901174])\n+Out[12]: array([0.97290577, 0.00500125])\n \n In [13]: print(existing)\n-[0.55876893 0.61901174 0. 0. ]\n+[0.97290577 0.00500125 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([1.06648364, 0.00958763])\n+Out[4]: array([0.89327527, 0.30236465])\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([4.80876402, 4.79917639], domain=[0., 9.], window=[-1., 1.], symbol='x')\n+Out[6]: Polynomial([4.32210337, 4.01973872], 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([0.00958763, 1.06648364], domain=[-1., 1.], window=[-1., 1.], symbol='x')\n+Out[7]: Polynomial([0.30236465, 0.89327527], 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([1.06648364, 0.00958763])\n+Out[4]: array([0.89327527, 0.30236465])\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([4.80876402, 4.79917639], domain=[0., 9.], window=[-1.,\n+Out[6]: Polynomial([4.32210337, 4.01973872], 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([0.00958763, 1.06648364], domain=[-1., 1.], window=[-1.,\n+Out[7]: Polynomial([0.30236465, 0.89327527], 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": "@@ -32324,21 +32324,21 @@\n \"001637457145670096\": 2315,\n \"001j\": [1596, 1653, 1710, 1767, 1824, 1879, 1893],\n \"002\": [1335, 1602, 1659, 1716, 1773, 1830, 1886],\n \"0024\": 477,\n \"003\": [2327, 2372, 2419],\n \"005\": 2188,\n \"0050000029\": [357, 359],\n+ \"00500125\": 2461,\n \"0050045159\": [357, 359],\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- \"00958763\": 2488,\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, 2323, 2329, 2367, 2373, 2414, 2420, 2525, 2657],\n \"010\": [653, 1602, 1659, 1716, 1773, 1830, 1886],\n \"0100\": 1519,\n \"01041667\": 1585,\n \"011\": [1602, 1659, 1716, 1773, 1830, 1886],\n@@ -32347,14 +32347,15 @@\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+ \"01973872\": 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@@ -32378,32 +32379,30 @@\n \"0396842\": 680,\n \"03t13\": 55,\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- \"04465839\": 2461,\n \"04551152e\": 2104,\n \"04719755\": 1911,\n- \"05\": [55, 91, 163, 410, 548, 669, 896, 1095, 1871, 2083, 2173, 2353, 2400, 2450, 2647],\n+ \"05\": [55, 91, 163, 410, 548, 669, 896, 1095, 1871, 2083, 2173, 2353, 2400, 2450, 2461, 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 \"0614962j\": [439, 453],\n \"0625\": [418, 624, 1645],\n \"06369197489564249\": 2458,\n \"06381726\": 349,\n \"0660\": [302, 2131],\n- \"06648364\": 2488,\n \"06959433e\": [420, 947],\n \"07\": [55, 164, 547, 896, 897, 1335, 2170, 2508],\n \"07106781e\": 514,\n \"07407407\": 1809,\n \"07779185\": 2458,\n \"07937323\": 524,\n \"07944154\": [657, 2654],\n@@ -32420,15 +32419,14 @@\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- \"09837248\": 2461,\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@@ -32566,15 +32564,15 @@\n \"1073741821\": [420, 421, 947, 948, 1923],\n \"1078\": 2622,\n \"108\": [524, 2463],\n \"10862\": 2538,\n \"10868\": 2538,\n \"1088311\": 2343,\n \"10898\": 2542,\n- \"109\": [136, 523, 2461, 2463],\n+ \"109\": [136, 523, 2463],\n \"10905\": 2538,\n \"10941\": 2328,\n \"10946\": 28,\n \"10947\": 2538,\n \"10959\": 2538,\n \"10960\": 2538,\n \"10961\": 2538,\n@@ -32656,15 +32654,15 @@\n \"11785\": 2543,\n \"11786\": 2543,\n \"1179\": 2463,\n \"118\": 2463,\n \"1180339887498949\": 2115,\n \"11803399\": 1228,\n \"11885628817151628\": 2458,\n- \"119\": [2461, 2616],\n+ \"119\": 2616,\n \"11902\": 2544,\n \"11981\": 2544,\n \"11982\": 2544,\n \"11985\": 2541,\n \"11986\": 2541,\n \"11987\": 2541,\n \"11992\": 2544,\n@@ -32749,15 +32747,14 @@\n \"13026\": 2549,\n \"13028\": 2549,\n \"13038\": 2549,\n \"13041\": 2549,\n \"13090\": [186, 827, 999, 1172, 1259, 1414, 1933],\n \"131\": [527, 2463],\n \"1312\": 485,\n- \"13149399\": 2461,\n \"13182611e\": [420, 947],\n \"132\": [527, 2330, 2374, 2421, 2463, 2636],\n \"1324274851176597e\": 1867,\n \"133\": [527, 2330, 2374, 2421],\n \"13392\": 2551,\n \"13394\": 2551,\n \"13396\": 2551,\n@@ -33219,15 +33216,15 @@\n \"17545176\": 1153,\n \"17568\": 2569,\n \"17577\": [2572, 2659],\n \"17580\": 2572,\n \"17582\": 2583,\n \"17586\": 2576,\n \"17596\": 2572,\n- \"176\": [2461, 2463],\n+ \"176\": 2463,\n \"17647\": 2569,\n \"17652\": 2569,\n \"17653\": 2569,\n \"17660\": 2569,\n \"17679\": 2570,\n \"17680\": 2570,\n \"177\": [514, 566, 680, 2658],\n@@ -33333,14 +33330,15 @@\n \"1875\": 1585,\n \"18763\": 2575,\n \"18764\": 2575,\n \"18768\": 2575,\n \"18769\": 2575,\n \"18794\": 2575,\n \"188\": [2463, 2636],\n+ \"18808335\": 2461,\n \"1885\": 2611,\n \"18874\": 2576,\n \"1887902\": 1911,\n \"18880\": 2576,\n \"18884\": 2583,\n \"18887\": 2575,\n \"189\": 2327,\n@@ -33634,15 +33632,14 @@\n \"20806\": 2584,\n \"20807\": 2584,\n \"20814\": 2584,\n \"20815\": 2584,\n \"20819\": 2584,\n \"20821\": 2588,\n \"20835\": 2588,\n- \"2084051\": 2461,\n \"20842\": 2585,\n \"20843\": 2585,\n \"20844\": 2585,\n \"20845\": 2585,\n \"20875\": 2588,\n \"20880\": 65,\n \"20906\": 2585,\n@@ -33665,15 +33662,15 @@\n \"20985\": 2585,\n \"20986\": 2585,\n \"20992\": 2585,\n \"20993\": 2588,\n \"20_ver\": 0,\n \"20count\": 141,\n \"20d03bcfd\": 0,\n- \"21\": [21, 26, 28, 30, 31, 40, 47, 54, 55, 58, 74, 98, 162, 163, 270, 336, 357, 359, 377, 388, 396, 403, 476, 477, 628, 661, 669, 880, 905, 944, 1069, 1229, 1312, 1466, 1869, 1881, 1986, 2091, 2168, 2172, 2208, 2225, 2230, 2237, 2238, 2342, 2343, 2463, 2513, 2515, 2517, 2519, 2567, 2568, 2572, 2583, 2585, 2588, 2594, 2627, 2628, 2632, 2634, 2636, 2640, 2641, 2648, 2653, 2656, 2664, 2665, 2667],\n+ \"21\": [21, 26, 28, 30, 31, 40, 47, 54, 55, 58, 74, 98, 162, 163, 270, 336, 357, 359, 377, 388, 396, 403, 476, 477, 628, 661, 669, 880, 905, 944, 1069, 1229, 1312, 1466, 1869, 1881, 1986, 2091, 2168, 2172, 2208, 2225, 2230, 2237, 2238, 2342, 2343, 2461, 2463, 2513, 2515, 2517, 2519, 2567, 2568, 2572, 2583, 2585, 2588, 2594, 2627, 2628, 2632, 2634, 2636, 2640, 2641, 2648, 2653, 2656, 2664, 2665, 2667],\n \"210\": 363,\n \"21001\": 2588,\n \"21029\": 2588,\n \"210306068529402873165736369884012333109\": [2275, 2280],\n \"21048\": 2586,\n \"211\": 2491,\n \"21106\": 2586,\n@@ -33690,15 +33687,15 @@\n \"21148\": 2586,\n \"21154\": 2588,\n \"21187\": 2588,\n \"21188\": 2588,\n \"21191\": 2587,\n \"21192\": 2587,\n \"21199\": 2622,\n- \"212\": [2461, 2622],\n+ \"212\": 2622,\n \"21243\": 2587,\n \"21245\": 2587,\n \"21262\": 2588,\n \"21275\": 2587,\n \"21277\": 2587,\n \"213\": [12, 2491],\n \"21336384\": 2658,\n@@ -33896,15 +33893,15 @@\n \"22972\": 2596,\n \"22976\": 2596,\n \"22982\": 2599,\n \"22989\": 2596,\n \"22997\": 2599,\n \"22998\": 2599,\n \"22e\": 457,\n- \"23\": [1, 8, 10, 18, 32, 43, 47, 54, 55, 58, 62, 63, 75, 79, 98, 135, 139, 163, 270, 287, 329, 336, 483, 513, 628, 669, 880, 905, 917, 1029, 1069, 1104, 1229, 1241, 1312, 1324, 1466, 1478, 1545, 1707, 1748, 1777, 1903, 1913, 1986, 1998, 2154, 2208, 2235, 2237, 2256, 2321, 2340, 2342, 2365, 2383, 2412, 2430, 2461, 2513, 2519, 2542, 2552, 2595, 2622, 2627, 2634, 2636, 2640, 2644, 2647, 2656, 2665],\n+ \"23\": [1, 8, 10, 18, 32, 43, 47, 54, 55, 58, 62, 63, 75, 79, 98, 135, 139, 163, 270, 287, 329, 336, 483, 513, 628, 669, 880, 905, 917, 1029, 1069, 1104, 1229, 1241, 1312, 1324, 1466, 1478, 1545, 1707, 1748, 1777, 1903, 1913, 1986, 1998, 2154, 2208, 2235, 2237, 2256, 2321, 2340, 2342, 2365, 2383, 2412, 2430, 2513, 2519, 2542, 2552, 2595, 2622, 2627, 2634, 2636, 2640, 2644, 2647, 2656, 2665],\n \"230\": 409,\n \"230000071797338e\": 477,\n \"23011\": 2599,\n \"23019\": 2599,\n \"23020\": 2599,\n \"23030\": 2596,\n \"23031\": 2596,\n@@ -34223,14 +34220,15 @@\n \"25186\": 2622,\n \"25188\": 2605,\n \"25189\": 2605,\n \"25190\": 2605,\n \"25191\": 2605,\n \"25192\": 2605,\n \"25193\": 2622,\n+ \"252\": 2461,\n \"25201\": 2605,\n \"25202\": 2605,\n \"25203\": 2605,\n \"25204\": 2605,\n \"25205\": 2605,\n \"25217\": 2605,\n \"25218\": 2605,\n@@ -34344,15 +34342,14 @@\n \"26268\": 2625,\n \"26285\": 2625,\n \"26292\": 2625,\n \"26313\": 2625,\n \"26388\": 2625,\n \"26393\": 2622,\n \"26452\": 2625,\n- \"265\": 2461,\n \"26501\": 2625,\n \"26579\": 2625,\n \"26580\": 2625,\n \"26590556\": 2634,\n \"26598632\": 1228,\n \"266\": 2463,\n \"26606588\": 533,\n@@ -34634,14 +34631,15 @@\n \"30000\": 533,\n \"3000488281\": 476,\n \"3003003\": 1999,\n \"3006\": 2614,\n \"3007\": 2614,\n \"301\": [438, 1923, 2477],\n \"30220482\": [2345, 2391, 2439],\n+ \"30236465\": 2488,\n \"30278462\": 1154,\n \"3039\": 2614,\n \"304\": 22,\n \"30464\": 2094,\n \"30498948e\": 2665,\n \"305\": [421, 948],\n \"3057\": 2615,\n@@ -34681,14 +34679,15 @@\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, 2636, 2638, 2640, 2644, 2645, 2647, 2648, 2651, 2656, 2657, 2658, 2665],\n \"320\": 1149,\n \"32000\": 2094,\n \"32119158\": 1867,\n+ \"32210337\": 2488,\n \"323\": [260, 421, 948, 1059, 1222, 1305, 1350, 1459, 1579, 1590, 1604, 1605, 1639, 1649, 1661, 1662, 1696, 1706, 1718, 1719, 1753, 1763, 1775, 1776, 1810, 1820, 1832, 1833, 1866, 1875, 1887, 1888, 1979, 2312],\n \"3263\": 2617,\n \"32767\": 535,\n \"32768\": 535,\n \"32_767\": 62,\n \"32_768\": 62,\n \"32bit\": [50, 61, 62, 2364, 2377, 2379, 2388, 2411, 2424, 2426, 2435, 2517, 2572, 2589],\n@@ -34738,15 +34737,15 @@\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@@ -34877,15 +34876,15 @@\n \"42667924\": 1154,\n \"4267\": 2617,\n \"4270\": 2617,\n \"4276\": 2617,\n \"429\": 136,\n \"4294967293\": 2638,\n \"4294967296\": [196, 836, 1008, 1179, 1266, 1421, 1940],\n- \"43\": [2208, 2461, 2583, 2634, 2640, 2656, 2665],\n+ \"43\": [2208, 2583, 2634, 2640, 2656, 2665],\n \"430148\": 2634,\n \"43014843\": 2634,\n \"43181166\": 2458,\n \"4354\": 2617,\n \"4359\": 2617,\n \"4368\": [287, 1241, 1324, 1478, 1998],\n \"4375\": 2491,\n@@ -34925,14 +34924,15 @@\n \"4520525295346629\": 1228,\n \"4532\": [409, 661, 2168],\n \"4545724517479104\": 2460,\n \"45560727e\": 54,\n \"456\": 1921,\n \"4567\": 2643,\n \"45674898e\": 566,\n+ \"45697908\": 2461,\n \"45a3d84\": 2521,\n \"46\": [409, 523, 905, 1707, 2204, 2208, 2640, 2656],\n \"460\": [2238, 2576],\n \"46009194e\": 566,\n \"4602\": 2618,\n \"4610935\": 457,\n \"4613\": 2618,\n@@ -34977,15 +34977,15 @@\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, 2461, 2567, 2568, 2640, 2656, 2665],\n+ \"49\": [71, 2208, 2323, 2367, 2414, 2567, 2568, 2640, 2656, 2665],\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@@ -35101,23 +35101,23 @@\n \"54999924\": 1247,\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+ \"55420097\": 2461,\n \"55458479\": 349,\n \"55490914e\": 2665,\n \"5555555555555554\": 1349,\n \"55627469\": 349,\n \"55645993\": 2634,\n \"5580\": 2535,\n- \"55876893\": 2461,\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@@ -35149,14 +35149,15 @@\n \"5910\": [287, 1241, 1324, 1478, 1998],\n \"595726\": 2634,\n \"59572603\": 2634,\n \"5969\": [99, 906],\n \"598150\": 2641,\n \"59815003\": 38,\n \"5982\": 2641,\n+ \"5988971\": 2461,\n \"59903635e\": 147,\n \"5d0\": 32,\n \"5e\": [114, 117, 119, 260, 669, 674, 675, 1059, 1222, 1305, 1350, 1459, 1579, 1590, 1596, 1604, 1605, 1639, 1649, 1653, 1661, 1662, 1696, 1706, 1710, 1718, 1719, 1753, 1763, 1767, 1775, 1776, 1810, 1820, 1824, 1832, 1833, 1866, 1875, 1879, 1887, 1888, 1893, 1979],\n \"5e16\": 55,\n \"5f\": 2086,\n \"5j\": [350, 541, 544, 1326, 1515, 2108, 2658],\n \"5th\": [513, 669, 2640],\n@@ -35171,24 +35172,23 @@\n \"60546483\": 523,\n \"60663578\": 2634,\n \"607\": [2339, 2382, 2429],\n \"60860684e\": 1594,\n \"609\": 2583,\n \"6094\": 2522,\n \"60x\": 2599,\n- \"61\": [13, 2656],\n+ \"61\": [13, 2461, 2656],\n \"610\": 28,\n \"61119\": 2098,\n \"614064523559687\": 2115,\n \"6143849206349179\": [1113, 1543],\n \"6176\": [99, 906],\n \"61799388\": 1911,\n \"618\": 669,\n \"6180\": [2353, 2400, 2450],\n- \"61901174\": 2461,\n \"61988120985\": [2323, 2367, 2414],\n \"61c54bbd\": 42,\n \"62\": [542, 968, 969, 2323, 2333, 2367, 2377, 2414, 2424, 2656],\n \"6208\": 2522,\n \"6227766\": 514,\n \"623\": [2394, 2444],\n \"62318272\": [2319, 2363, 2410],\n@@ -35228,15 +35228,15 @@\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\": 2656,\n+ \"65\": [2461, 2656],\n \"650\": 2618,\n \"6500\": 2522,\n \"6501\": 2522,\n \"65028784\": 2665,\n \"65143654\": 1154,\n \"6515\": [2353, 2400, 2450],\n \"65200189e\": 566,\n@@ -35337,26 +35337,26 @@\n \"6840\": 2524,\n \"6843\": 2524,\n \"68456316\": [2339, 2352, 2382, 2389, 2399, 2429, 2436, 2449],\n \"68482974\": 1153,\n \"6884\": 2524,\n \"68862757\": 660,\n \"6888893\": [2352, 2399, 2449],\n- \"6899817\": 2461,\n \"69\": [58, 431, 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 \"6937\": 2524,\n \"6942\": 2524,\n \"6943\": 2524,\n+ \"69487323\": 2461,\n \"6949\": 2524,\n \"6950\": 2524,\n \"6952\": 2524,\n \"69583040e\": [420, 947],\n \"69646919\": 1153,\n \"69736803\": [349, 2457, 2638],\n \"699\": 520,\n@@ -35387,17 +35387,17 @@\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- \"721\": 2461,\n \"721fc64\": 13,\n \"72375\": 1644,\n+ \"724\": 2461,\n \"72538256\": [103, 126],\n \"72686684e\": 566,\n \"72717132\": 2658,\n \"72727273\": 136,\n \"72847407\": 1154,\n \"729\": 2665,\n \"72904971\": 1153,\n@@ -35510,15 +35510,14 @@\n \"7954\": 2527,\n \"7955\": 2527,\n \"79579319e\": 1867,\n \"79694221e\": 1586,\n \"7972\": 2527,\n \"7976931348623157e\": 1335,\n \"79769313e\": 1335,\n- \"79917639\": 2488,\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, 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2648, 2652, 2654, 2656, 2657, 2658, 2659, 2664, 2665],\n \"80\": [69, 396, 409, 446, 977, 2248, 2346, 2357, 2383, 2392, 2404, 2430, 2441, 2454, 2588, 2622, 2647, 2648, 2656],\n@@ -35530,15 +35529,14 @@\n \"8010\": 2527,\n \"8020\": 2527,\n \"8024\": 2527,\n \"8031\": 2527,\n \"804\": 2508,\n \"8044\": 2527,\n \"8058837395885292\": 666,\n- \"80876402\": 2488,\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@@ -35561,15 +35559,15 @@\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- \"84\": [2461, 2656, 2658],\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 \"84147098j\": 2665,\n@@ -35584,24 +35582,25 @@\n \"85602287\": [2335, 2378, 2425],\n \"857\": 410,\n \"8570331885190563e\": [648, 653],\n \"85715698e\": 2171,\n \"8577\": 2539,\n \"85859792\": [349, 2457, 2638],\n \"8595784\": 2634,\n- \"86\": [59, 88, 101, 103, 106, 126, 131, 542, 968, 969, 2323, 2367, 2414, 2491, 2656],\n+ \"86\": [59, 88, 101, 103, 106, 126, 131, 542, 968, 969, 2323, 2367, 2414, 2461, 2491, 2656],\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 \"86820401\": [2345, 2391, 2439],\n \"86864911e\": 1586,\n+ \"86917627\": 2461,\n \"87\": [2616, 2656],\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@@ -35616,14 +35615,15 @@\n \"88975\": 1644,\n \"89\": [28, 2091, 2643, 2656],\n \"890\": 2643,\n \"8900451\": 1154,\n \"89086505\": [2352, 2399, 2449],\n \"89206682e\": 2104,\n \"8922078\": 2458,\n+ \"89327527\": 2488,\n \"89442719\": 642,\n \"89442719j\": 642,\n \"89721355\": 349,\n \"89804309e\": 2104,\n \"89920014\": [2319, 2363, 2410],\n \"8999999999999999\": 2107,\n \"8b2\": 2554,\n@@ -35657,15 +35657,15 @@\n \"9262\": 2532,\n \"9263\": 2532,\n \"9267\": 2532,\n \"92676499\": [349, 2638],\n \"927\": [539, 554],\n \"92771843\": 1154,\n \"9299\": 2532,\n- \"93\": [2461, 2656],\n+ \"93\": 2656,\n \"9304e\": 2091,\n \"931\": 2587,\n \"9317\": 2532,\n \"9319\": 2532,\n \"9339\": 2532,\n \"9340\": 2532,\n \"934284\": 349,\n@@ -35676,15 +35676,15 @@\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, 2634, 2656],\n+ \"94\": [409, 669, 2461, 2634, 2656],\n \"940\": 2587,\n \"941257\": 2634,\n \"94125714\": 2634,\n \"94708397920832\": 2641,\n \"9475673279178444\": 2348,\n \"94864945\": 2665,\n \"94909878\": [2387, 2434],\n@@ -35710,14 +35710,15 @@\n \"969792\": 2634,\n \"96e7\": 42,\n \"97\": [2463, 2634, 2656, 2665],\n \"9700\": 2665,\n \"9701\": 2665,\n \"9702\": 2665,\n \"97074098\": 349,\n+ \"97290577\": 2461,\n \"973\": [941, 1114, 1123, 1124, 1131],\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@@ -35733,15 +35734,15 @@\n \"97719\": 1644,\n \"9772\": 2534,\n \"9794\": 2534,\n \"9797\": 2665,\n \"97974649\": 524,\n \"9798\": 2665,\n \"9799\": 2665,\n- \"98\": [481, 647, 1157, 2634, 2656, 2665],\n+ \"98\": [481, 647, 1157, 2461, 2634, 2656, 2665],\n \"9800\": 2665,\n \"9801\": 2665,\n \"9802\": 2665,\n \"98024613\": 680,\n \"9807642\": 1153,\n \"981\": 2592,\n \"98136677\": 523,\n@@ -35762,15 +35763,14 @@\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- \"9949636\": 2461,\n \"99507202\": 349,\n \"99734545\": 1154,\n \"998\": 2535,\n \"99822295\": [103, 126],\n \"99827656\": 1754,\n \"99885316e\": 566,\n \"999\": [543, 844, 864, 887, 1020, 1049, 1077, 1125, 2535, 2643],\n"}]}]}]}]}]}