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-7.3 ms +- 72.9 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-14.6 ms +- 36.9 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+4.15 ms +- 79.9 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+6.2 ms +- 22.2 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-6.17 ms +- 61.5 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-17.4 ms +- 223 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+3.46 ms +- 15.6 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+5.83 ms +- 11.3 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-27.1 ms +- 302 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-32.6 ms +- 522 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+12.1 ms +- 18.6 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+14.2 ms +- 12 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([0.23463919, 0.72393835, 0.14778879])\n+Out[7]: array([0.62899335, 0.03774 , 0.21407664])\n \n In [8]: rng.random(3, dtype=np.float32)\n-Out[8]: array([0.87651783, 0.8591692 , 0.7715133 ], dtype=float32)\n+Out[8]: array([0.32505184, 0.85750914, 0.6715027 ], dtype=float32)\n \n In [9]: rng.integers(0, 256, size=3, dtype=np.uint8)\n-Out[9]: array([153, 30, 207], dtype=uint8)\n+Out[9]: array([232, 105, 192], 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([0.64358556, 0.04163277])\n+Out[12]: array([0.35711538, 0.22780344])\n \n In [13]: print(existing)\n-[0.64358556 0.04163277 0. 0. ]\n+[0.35711538 0.22780344 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([0.98287535, 0.47084069])\n+Out[4]: array([ 1.1262849 , -0.14201884])\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([4.89377979, 4.42293909], domain=[0., 9.], window=[-1., 1.], symbol='x')\n+Out[6]: Polynomial([4.9262632 , 5.06828204], 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([0.47084069, 0.98287535], domain=[-1., 1.], window=[-1., 1.], symbol='x')\n+Out[7]: Polynomial([-0.14201884, 1.1262849 ], 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([0.98287535, 0.47084069])\n+Out[4]: array([ 1.1262849 , -0.14201884])\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([4.89377979, 4.42293909], domain=[0., 9.], window=[-1.,\n+Out[6]: Polynomial([4.9262632 , 5.06828204], 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([0.47084069, 0.98287535], domain=[-1., 1.], window=[-1.,\n+Out[7]: Polynomial([-0.14201884, 1.1262849 ], 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": "@@ -32373,22 +32373,22 @@\n \"02785049\": 1867,\n \"02i\": [513, 2644],\n \"03\": [55, 67, 163, 566, 669, 1335, 1586, 1816, 2658],\n \"03125\": [1585, 2491],\n \"0326911\": [2335, 2378, 2425],\n \"0361\": 2607,\n \"03703704\": 1809,\n+ \"03774\": 2461,\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 \"0400\": 360,\n \"04097352\": 2635,\n- \"04163277\": 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, 2353, 2400, 2450, 2648],\n \"0500\": 360,\n \"05093587\": 2635,\n@@ -32399,14 +32399,15 @@\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+ \"06828204\": 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, 2655],\n@@ -32524,15 +32525,15 @@\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@@ -32722,14 +32723,15 @@\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],\n \"1261\": 2612,\n+ \"1262849\": 2488,\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 \"12769\": 2548,\n@@ -32851,14 +32853,15 @@\n \"14194\": 2555,\n \"14197\": 2560,\n \"14198\": 2555,\n \"14199\": 2555,\n \"142\": 655,\n \"14200\": 2555,\n \"14201\": 2555,\n+ \"14201884\": 2488,\n \"14211\": 2553,\n \"14227\": 2560,\n \"14228\": 2555,\n \"14236\": 2555,\n \"14237\": 2555,\n \"14248\": 2560,\n \"14255\": 2560,\n@@ -32941,15 +32944,14 @@\n \"14717\": 2560,\n \"14718\": 2560,\n \"14720\": 2560,\n \"14730\": 2560,\n \"14758\": 2558,\n \"14771\": 2560,\n \"14777\": 2560,\n- \"14778879\": 2461,\n \"14781\": 2558,\n \"14787\": 2569,\n \"148\": [2344, 2386, 2433, 2463],\n \"14812\": 3,\n \"148293216\": 2666,\n \"14841\": 2560,\n \"14851\": 2558,\n@@ -33016,15 +33018,15 @@\n \"15245\": 2561,\n \"15246\": 2561,\n \"15247\": 2561,\n \"15250\": 2561,\n \"15251\": 2566,\n \"15255\": 2566,\n \"15271\": 2576,\n- \"153\": [2461, 2583],\n+ \"153\": 2583,\n \"15302337\": 523,\n \"1534\": 485,\n \"15355\": 2566,\n \"15385\": 2566,\n \"154\": [2463, 2666],\n \"15427\": 2566,\n \"15463\": 2566,\n@@ -33374,15 +33376,15 @@\n \"19062\": 2583,\n \"1908\": [2353, 2400, 2450],\n \"19083\": 2583,\n \"19135\": 2583,\n \"19151\": 2583,\n \"191614240\": 95,\n \"1918\": 2612,\n- \"192\": [69, 669, 1519, 2463],\n+ \"192\": [69, 669, 1519, 2461, 2463],\n \"19211\": 2583,\n \"192163377\": 2098,\n \"19226\": 2588,\n \"1923875335537315\": [2352, 2389, 2399, 2436, 2449],\n \"19249760\": [420, 947],\n \"19259\": 2583,\n \"193\": [2463, 2637],\n@@ -33609,15 +33611,15 @@\n \"2052\": 2615,\n \"20580\": 2588,\n \"20589\": 2588,\n \"206\": 2463,\n \"20613\": 2581,\n \"20618\": 2581,\n \"2063\": 2612,\n- \"207\": [2461, 2463],\n+ \"207\": 2463,\n \"20702\": 2584,\n \"20703\": 2584,\n \"20704\": 2584,\n \"20714\": 2584,\n \"20722\": 2588,\n \"20724\": 2584,\n \"20725\": 2584,\n@@ -33703,14 +33705,15 @@\n \"21277\": 2587,\n \"213\": [12, 2491],\n \"21336384\": 2659,\n \"2134086255804012e\": 1923,\n \"21350\": 2587,\n \"21354\": 2588,\n \"21386\": 2587,\n+ \"21407664\": 2461,\n \"21437\": 2594,\n \"21438\": 2587,\n \"21444\": 2587,\n \"21445\": 2587,\n \"21446\": 2587,\n \"21447\": 2587,\n \"21448\": 2587,\n@@ -33749,15 +33752,15 @@\n \"219\": 2463,\n \"21925\": 2594,\n \"21949\": 2589,\n \"21951\": 2589,\n \"21952\": 2589,\n \"21976\": 2594,\n \"21995\": 2594,\n- \"22\": [21, 22, 29, 30, 40, 47, 52, 54, 55, 58, 59, 98, 107, 108, 109, 163, 270, 336, 378, 425, 485, 628, 658, 669, 880, 905, 1045, 1069, 1113, 1211, 1229, 1294, 1312, 1336, 1337, 1340, 1341, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 1358, 1448, 1466, 1514, 1521, 1522, 1543, 1591, 1905, 1908, 1913, 1968, 1986, 2091, 2208, 2236, 2237, 2342, 2513, 2517, 2519, 2534, 2588, 2635, 2637, 2641, 2657, 2666],\n+ \"22\": [21, 22, 29, 30, 40, 47, 52, 54, 55, 58, 59, 98, 107, 108, 109, 163, 270, 336, 378, 425, 485, 628, 658, 669, 880, 905, 1045, 1069, 1113, 1211, 1229, 1294, 1312, 1336, 1337, 1340, 1341, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 1358, 1448, 1466, 1514, 1521, 1522, 1543, 1591, 1905, 1908, 1913, 1968, 1986, 2091, 2208, 2236, 2237, 2342, 2461, 2513, 2517, 2519, 2534, 2588, 2635, 2637, 2641, 2657, 2666],\n \"220\": [2238, 2576],\n \"22004\": 2594,\n \"22014\": 2594,\n \"22030\": 2590,\n \"22031\": 2590,\n \"22032\": 2590,\n \"22033\": 2590,\n@@ -33792,15 +33795,14 @@\n \"22221\": 2591,\n \"22222\": 2591,\n \"222222\": 1335,\n \"22223\": 2591,\n \"22224\": 2591,\n \"22228\": 2594,\n \"22230\": 2591,\n- \"223\": 2461,\n \"22313\": 2594,\n \"22314355\": 2655,\n \"22315\": 2599,\n \"22316\": 2594,\n \"22357\": 2594,\n \"22368\": 2592,\n \"22370\": 2592,\n@@ -33860,14 +33862,15 @@\n \"22707\": 2599,\n \"22723872\": 349,\n \"22733602246716966\": 2457,\n \"22740995\": 1149,\n \"22769\": 2599,\n \"22776\": 2599,\n \"22776602\": [680, 2659],\n+ \"22780344\": 2461,\n \"22786\": 2599,\n \"228\": 2463,\n \"22820\": 2595,\n \"22830\": 2595,\n \"22831\": 2595,\n \"22832\": 2595,\n \"22834\": 2595,\n@@ -33923,14 +33926,15 @@\n \"23148\": 2596,\n \"23149\": 2596,\n \"23150\": 2596,\n \"23161\": 2596,\n \"2317\": 2620,\n \"23194\": 2597,\n \"23195\": 2599,\n+ \"232\": 2461,\n \"23204345\": [2345, 2391, 2439],\n \"23206\": 2597,\n \"23207\": 2597,\n \"23208\": 2597,\n \"23221\": 2597,\n \"23226\": 2597,\n \"23229\": 2599,\n@@ -33952,15 +33956,14 @@\n \"23371\": 2599,\n \"23376\": 2599,\n \"23385948e\": 54,\n \"234\": 55,\n \"23403\": 2599,\n \"2345672e\": 2172,\n \"234567e\": 2172,\n- \"23463919\": 2461,\n \"23480\": 2599,\n \"23528\": 2599,\n \"23543\": 2597,\n \"23544\": 2597,\n \"23598776\": 1911,\n \"23601\": 2599,\n \"23606798\": 653,\n@@ -34396,15 +34399,15 @@\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@@ -34650,24 +34653,23 @@\n \"2nd\": [513, 641, 642, 655, 658, 669, 1526, 2335, 2378, 2425, 2637, 2641, 2666],\n \"2to3\": 2616,\n \"2x\": [1527, 1542, 2357, 2404, 2454, 2488, 2491, 2616, 2619],\n \"2x2\": 47,\n \"2x3\": [47, 72, 2665],\n \"2x3x5\": 336,\n \"3\": [1, 2, 5, 10, 11, 12, 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2666,\n \"305\": [421, 948],\n@@ -34704,19 +34706,20 @@\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, 2633, 2637, 2639, 2641, 2645, 2646, 2648, 2649, 2652, 2657, 2658, 2659, 2666],\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+ \"32505184\": 2461,\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@@ -34765,15 +34768,16 @@\n \"35\": [409, 489, 669, 870, 1056, 2204, 2325, 2369, 2416, 2572, 2635, 2641, 2657, 2666],\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, 2461, 2463, 2491, 2536, 2649, 2657, 2659, 2666],\n+ \"35711538\": 2461,\n+ \"36\": [58, 137, 355, 1752, 1761, 2204, 2225, 2323, 2367, 2414, 2463, 2491, 2536, 2649, 2657, 2659, 2666],\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@@ -34887,15 +34891,14 @@\n \"42\": [31, 58, 63, 147, 349, 669, 896, 897, 974, 1029, 2090, 2208, 2256, 2332, 2376, 2423, 2457, 2566, 2605, 2622, 2635, 2639, 2657, 2664, 2665, 2666],\n \"420\": [2238, 2576],\n \"42016704\": 2666,\n \"4206\": 2617,\n \"4220\": 2617,\n \"4223\": 2617,\n \"4225\": 2617,\n- \"42293909\": 2488,\n \"423\": 55,\n \"42310646\": 1153,\n \"42332645\": 2666,\n \"42457905e\": 1586,\n \"425\": [523, 524],\n \"4253\": 2617,\n \"4254\": 2617,\n@@ -34954,15 +34957,15 @@\n \"4532\": [409, 661, 2168],\n \"4545724517479104\": 2460,\n \"45560727e\": 54,\n \"456\": 1921,\n \"4567\": 2644,\n \"45674898e\": 566,\n \"45a3d84\": 2521,\n- \"46\": [409, 523, 905, 1707, 2204, 2208, 2641, 2657],\n+ \"46\": [409, 523, 905, 1707, 2204, 2208, 2461, 2641, 2657],\n \"460\": [2238, 2576],\n \"46009194e\": 566,\n \"4602\": 2618,\n \"4610935\": 457,\n \"4613\": 2618,\n \"4628\": 2618,\n \"46351241j\": 2081,\n@@ -34977,15 +34980,14 @@\n \"46755891e\": 54,\n \"468\": [136, 147],\n \"4685006\": [2352, 2399, 2449],\n \"4686\": 12,\n \"46957616e\": [470, 1899, 1900],\n \"47\": [52, 2208, 2323, 2367, 2414, 2657, 2666],\n \"4702687338396767\": 2348,\n- \"47084069\": 2488,\n \"471\": [136, 147, 2463],\n \"47108547995356098\": [2345, 2391, 2439],\n \"47140452j\": 2491,\n \"472\": 55,\n \"4722\": 2618,\n \"4723\": 2621,\n \"4730\": [409, 661, 2168],\n@@ -35079,15 +35081,14 @@\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, 2554, 2635, 2641, 2648, 2657, 2659, 2660, 2666],\n \"5203\": 2620,\n- \"522\": 2461,\n \"5225\": 2620,\n \"5231\": 2620,\n \"52338984\": [2345, 2391, 2439],\n \"52359878\": 1911,\n \"52380952e\": 1816,\n \"5240\": 2620,\n \"5251\": 2620,\n@@ -35200,15 +35201,15 @@\n \"60546483\": 523,\n \"60663578\": 2635,\n \"607\": [2339, 2382, 2429],\n \"60860684e\": 1594,\n \"609\": 2583,\n \"6094\": 2522,\n \"60x\": 2599,\n- \"61\": [13, 2461, 2657],\n+ \"61\": [13, 2657],\n \"610\": 28,\n \"61119\": 2098,\n \"614064523559687\": 2115,\n \"6143849206349179\": [1113, 1543],\n \"6176\": [99, 906],\n \"61799388\": 1911,\n \"618\": 669,\n@@ -35221,28 +35222,28 @@\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+ \"62899335\": 2461,\n \"62949953e\": 645,\n \"63\": [58, 514, 669, 1748, 1777, 2336, 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 \"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- \"64358556\": 2461,\n \"64386512\": 349,\n \"64402274e\": 660,\n \"6446\": [2550, 2554],\n \"646\": [2517, 2576],\n \"6460\": 2522,\n \"6462\": 2522,\n \"6467\": 2522,\n@@ -35333,14 +35334,15 @@\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 \"67046769e\": 147,\n+ \"6715027\": 2461,\n \"6717\": 2522,\n \"6718\": 2522,\n \"6719\": 2522,\n \"6721\": 2522,\n \"6726\": 2522,\n \"6735\": 2522,\n \"6747\": 2522,\n@@ -35412,20 +35414,19 @@\n \"718281\": 431,\n \"71828182845904523536028747135266249775724709369995\": 76,\n \"71828183\": [38, 2666],\n \"718282\": 2642,\n \"7183\": 2642,\n \"7185\": [99, 906],\n \"71946897\": 1153,\n- \"72\": [13, 355, 544, 669, 1764, 2461, 2463, 2572, 2657, 2659],\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- \"72393835\": 2461,\n \"72538256\": [103, 126],\n \"72686684e\": 566,\n \"72717132\": 2659,\n \"72727273\": 136,\n \"72847407\": 1154,\n \"729\": 2666,\n \"72904971\": 1153,\n@@ -35485,15 +35486,14 @@\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 \"77086955\": 1526,\n- \"7715133\": 2461,\n \"7724\": 2526,\n \"7725\": [2353, 2400, 2450],\n \"7731\": 2526,\n \"7736\": 2527,\n \"7737\": 2526,\n \"7738\": 2527,\n \"77395605\": [349, 2457, 2639],\n@@ -35521,15 +35521,15 @@\n \"78539816\": [94, 104, 105, 129, 130, 2238],\n \"78539816339744828\": [104, 129],\n \"7854j\": [413, 619],\n \"78571429e\": 1816,\n \"78606431\": [349, 2457, 2639],\n \"789\": 2644,\n \"7896\": 2527,\n- \"79\": [13, 87, 100, 104, 129, 2657],\n+ \"79\": [13, 87, 100, 104, 129, 2461, 2657],\n \"79033856e\": 1149,\n \"7904\": 2527,\n \"7917\": 2527,\n \"7919\": 2527,\n \"7920\": [1212, 2527],\n \"7932\": 2527,\n \"7939\": 2527,\n@@ -35580,15 +35580,15 @@\n \"8255\": 2566,\n \"826716f\": 2521,\n \"82743037\": 524,\n \"82770259\": 2666,\n \"8277025938204418\": 2666,\n \"827941\": [514, 680, 2659],\n \"82842712\": [642, 644],\n- \"83\": [2105, 2167, 2353, 2400, 2450, 2554, 2657],\n+ \"83\": [2105, 2167, 2353, 2400, 2450, 2461, 2554, 2657],\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@@ -35608,17 +35608,17 @@\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+ \"85750914\": 2461,\n \"8577\": 2539,\n \"85859792\": [349, 2457, 2639],\n- \"8591692\": 2461,\n \"8595784\": 2635,\n \"86\": [59, 88, 101, 103, 106, 126, 131, 542, 968, 969, 2323, 2367, 2414, 2491, 2657],\n \"8601\": [55, 62, 67, 2613],\n \"86260211e\": 54,\n \"8630830\": 13,\n \"86399\": 55,\n \"86400\": 55,\n@@ -35626,15 +35626,14 @@\n \"8660254\": 2103,\n \"86820401\": [2345, 2391, 2439],\n \"86864911e\": 1586,\n \"87\": [2616, 2657],\n \"875\": [478, 2491],\n \"8755\": [186, 827, 999, 1172, 1259, 1414, 1933],\n \"87649168120691\": 674,\n- \"87651783\": 2461,\n \"8770\": [2353, 2400, 2450],\n \"88\": [408, 2462, 2463, 2657, 2659, 2668],\n \"8801\": [99, 906],\n \"88031624\": 2666,\n \"88079259\": 533,\n \"881943016134134\": 666,\n \"88622693\": 1642,\n@@ -35645,15 +35644,14 @@\n \"88975\": 1644,\n \"89\": [28, 2091, 2644, 2657],\n \"890\": 2644,\n \"8900451\": 1154,\n \"89086505\": [2352, 2399, 2449],\n \"89206682e\": 2104,\n \"8922078\": 2458,\n- \"89377979\": 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@@ -35681,14 +35679,15 @@\n \"92362781e\": 2104,\n \"92387953\": 642,\n \"92387953j\": 642,\n \"9240\": 2532,\n \"9255\": 2532,\n \"9261\": 2532,\n \"9262\": 2532,\n+ \"9262632\": 2488,\n \"9263\": 2532,\n \"9267\": 2532,\n \"92676499\": [349, 2639],\n \"927\": [539, 554],\n \"92771843\": 1154,\n \"9299\": 2532,\n \"93\": 2657,\n@@ -35771,15 +35770,14 @@\n \"9800\": 2666,\n \"9801\": 2666,\n \"9802\": 2666,\n \"98024613\": 680,\n \"9807642\": 1153,\n \"981\": 2592,\n \"98136677\": 523,\n- \"98287535\": 2488,\n \"987\": 28,\n \"987654321\": 2393,\n \"98935825\": 2666,\n \"9897\": 2666,\n \"9898\": 2666,\n \"9899\": [105, 130, 2666],\n \"99\": [12, 302, 408, 544, 672, 1096, 1906, 2131, 2460, 2635, 2657, 2658, 2666],\n"}]}]}]}]}]}