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-939 us +- 44.3 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-2.42 ms +- 36.5 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+1.03 ms +- 39.6 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+2.43 ms +- 41.9 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-796 us +- 18.8 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-1.69 ms +- 22 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+851 us +- 18 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+1.7 ms +- 34.5 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-2.92 ms +- 1.41 ms per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-4.1 ms +- 28.5 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+2.46 ms +- 34.5 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+4.1 ms +- 20.7 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([0.55792744, 0.10045431, 0.39091772])\n+Out[7]: array([0.12730094, 0.86732915, 0.29751739])\n \n In [8]: rng.random(3, dtype=np.float32)\n-Out[8]: array([0.7786327 , 0.44079942, 0.11658084], dtype=float32)\n+Out[8]: array([0.07399744, 0.87415296, 0.9917921 ], dtype=float32)\n \n In [9]: rng.integers(0, 256, size=3, dtype=np.uint8)\n-Out[9]: array([192, 232, 195], dtype=uint8)\n+Out[9]: array([217, 193, 195], 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([0.81716537, 0.98353266])\n+Out[12]: array([0.23968024, 0.57921891])\n \n In [13]: print(existing)\n-[0.81716537 0.98353266 0. 0. ]\n+[0.23968024 0.57921891 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([0.83003832, 0.81698516])\n+Out[4]: array([ 1.03419431, -0.3995521 ])\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([4.55215758, 3.73517242], domain=[0., 9.], window=[-1., 1.], symbol='x')\n+Out[6]: Polynomial([4.25432228, 4.65387438], 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([0.81698516, 0.83003832], domain=[-1., 1.], window=[-1., 1.], symbol='x')\n+Out[7]: Polynomial([-0.3995521 , 1.03419431], 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([0.83003832, 0.81698516])\n+Out[4]: array([ 1.03419431, -0.3995521 ])\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([4.55215758, 3.73517242], domain=[0., 9.], window=[-1.,\n+Out[6]: Polynomial([4.25432228, 4.65387438], 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([0.81698516, 0.83003832], domain=[-1., 1.], window=[-1.,\n+Out[7]: Polynomial([-0.3995521 , 1.03419431], 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": "@@ -32368,17 +32368,18 @@\n \"0253\": 2652,\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+ \"03\": [55, 67, 163, 566, 669, 1335, 1586, 1816, 2461, 2658],\n \"03125\": [1585, 2491],\n \"0326911\": [2335, 2378, 2425],\n+ \"03419431\": 2488,\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@@ -32401,14 +32402,15 @@\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+ \"07399744\": 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, 2525, 2659],\n \"0800\": 2525,\n \"08187135\": 54,\n@@ -32492,15 +32494,14 @@\n \"100000\": [2327, 2336, 2337, 2346, 2354, 2357, 2372, 2379, 2380, 2392, 2401, 2404, 2419, 2426, 2427, 2441, 2451, 2454, 2461],\n \"1000000\": [357, 359, 2338, 2344, 2346, 2349, 2351, 2353, 2381, 2386, 2392, 2396, 2398, 2400, 2428, 2433, 2441, 2446, 2448, 2450],\n \"10000000\": [2312, 2460],\n \"10000000000\": [896, 897],\n \"1000000000000000000\": 2648,\n \"1000j\": 514,\n \"1001\": 2535,\n- \"10045431\": 2461,\n \"100_000\": [669, 2588],\n \"100j\": 1909,\n \"100x5\": 652,\n \"101\": [86, 137, 138, 143, 145, 570, 1325, 2077, 2463, 2666],\n \"1010\": [145, 1519, 2077],\n \"10100\": [143, 570],\n \"1015\": 2592,\n@@ -32628,15 +32629,14 @@\n \"1151\": 657,\n \"11525\": 2547,\n \"116\": 2463,\n \"11625\": [2543, 2544, 2545, 2546],\n \"11647\": 2543,\n \"11648\": 2543,\n \"11657\": 2543,\n- \"11658084\": 2461,\n \"11659149\": [2345, 2391, 2439],\n \"11661\": 2543,\n \"11665\": 2543,\n \"11675684e\": 1586,\n \"11682\": 2543,\n \"11698\": 2543,\n \"11700\": 2543,\n@@ -32726,14 +32726,15 @@\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 \"12658\": 2560,\n \"12697628\": 2635,\n \"127\": [62, 66, 514, 863, 1048, 1102, 1116, 1904, 2301, 2302, 2462, 2463, 2464, 2583, 2639],\n+ \"12730094\": 2461,\n \"12736\": [2548, 2549],\n \"12767\": 2548,\n \"12768\": 2548,\n \"12769\": 2548,\n \"12773\": 2548,\n \"128\": [56, 62, 69, 114, 514, 863, 1048, 1098, 1116, 1335, 1904, 2091, 2162, 2270, 2275, 2280, 2285, 2290, 2299, 2300, 2301, 2302, 2303, 2348, 2458, 2462, 2463, 2464, 2525, 2535, 2566, 2583, 2622, 2639, 2648],\n \"12811363\": [349, 2457, 2639],\n@@ -33374,22 +33375,22 @@\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, 2461, 2463],\n+ \"192\": [69, 669, 1519, 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+ \"193\": [2461, 2463, 2637],\n \"19311\": 2577,\n \"1932\": [2359, 2406, 2456],\n \"19324\": 2577,\n \"19330\": 2577,\n \"19342\": 2577,\n \"19343\": 2577,\n \"19347\": 2577,\n@@ -33515,15 +33516,15 @@\n \"1l_0\": 1822,\n \"1rc1\": 577,\n \"1st\": [36, 74, 642, 2616, 2637, 2641],\n \"1th\": [661, 2168],\n \"1type\": 2554,\n \"1xn\": 2665,\n \"2\": [0, 1, 2, 4, 5, 9, 12, 13, 14, 19, 20, 24, 25, 26, 29, 30, 31, 32, 34, 36, 37, 38, 43, 47, 48, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 65, 66, 68, 69, 70, 72, 73, 74, 75, 76, 79, 86, 88, 89, 90, 95, 96, 97, 98, 99, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 163, 167, 168, 169, 170, 171, 176, 177, 184, 185, 186, 194, 196, 204, 210, 213, 214, 215, 227, 229, 234, 238, 239, 251, 261, 262, 263, 264, 270, 278, 280, 284, 287, 290, 293, 301, 303, 315, 316, 328, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 389, 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2430, 2435, 2438, 2461, 2462, 2463, 2470, 2513, 2517, 2519, 2533, 2535, 2542, 2560, 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@@ -33733,14 +33734,15 @@\n \"2155\": [305, 2134],\n \"21595\": 2594,\n \"216\": 2666,\n \"21623\": [2588, 2594],\n \"21627\": 2594,\n \"21645\": 2594,\n \"21663\": 2588,\n+ \"217\": 2461,\n \"21760\": 2622,\n \"218\": [566, 2463],\n \"21807\": 2594,\n \"2184\": 2225,\n \"21866\": 2589,\n \"21867\": 2589,\n \"21868\": 2589,\n@@ -33749,15 +33751,15 @@\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, 2461, 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, 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@@ -33922,15 +33924,14 @@\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@@ -33989,14 +33990,15 @@\n \"23890\": 2598,\n \"23919\": 2622,\n \"23921\": 2622,\n \"23922\": 2622,\n \"23936\": 2622,\n \"2394691\": 2312,\n \"23968\": 2600,\n+ \"23968024\": 2461,\n \"23994\": 2598,\n \"23998\": 2622,\n \"23e\": 477,\n \"23e24\": 477,\n \"24\": [10, 38, 47, 54, 55, 56, 58, 59, 62, 67, 98, 107, 108, 355, 356, 358, 408, 409, 477, 528, 531, 541, 542, 567, 638, 661, 662, 664, 838, 905, 939, 964, 968, 969, 1010, 1133, 1144, 1546, 1577, 1607, 1664, 1721, 1778, 1835, 1864, 1883, 1902, 2100, 2114, 2168, 2175, 2200, 2208, 2223, 2225, 2226, 2230, 2237, 2247, 2342, 2463, 2513, 2519, 2543, 2555, 2622, 2623, 2635, 2641, 2645, 2649, 2652, 2657, 2659, 2666, 2668],\n \"240\": [57, 363],\n \"24011\": 2622,\n@@ -34255,14 +34257,15 @@\n \"25388\": 2622,\n \"254\": [143, 570],\n \"25409\": 2622,\n \"25419\": 2605,\n \"25420\": 2605,\n \"25422\": 2605,\n \"25428\": 2605,\n+ \"25432228\": 2488,\n \"25434\": 2622,\n \"25437\": 2622,\n \"25441\": 2622,\n \"25452\": 2605,\n \"25458\": 2605,\n \"25463\": 2622,\n \"25465\": 2605,\n@@ -34510,15 +34513,15 @@\n \"27t00\": 360,\n \"27t01\": 360,\n \"27t02\": 360,\n \"27t04\": 360,\n \"27t05\": 360,\n \"27t06\": 360,\n \"27t07\": 360,\n- \"28\": [36, 54, 55, 146, 409, 661, 1695, 1704, 1707, 1862, 2168, 2208, 2225, 2461, 2463, 2513, 2538, 2539, 2540, 2543, 2629, 2641, 2649, 2657, 2659, 2666],\n+ \"28\": [36, 54, 55, 146, 409, 661, 1695, 1704, 1707, 1862, 2168, 2208, 2225, 2463, 2513, 2538, 2539, 2540, 2543, 2629, 2641, 2649, 2657, 2659, 2666],\n \"28000000e\": 1335,\n \"2800000e\": 1335,\n \"28006\": 2630,\n \"28007\": 2630,\n \"2801\": 2613,\n \"28021\": 2630,\n \"28044\": 2630,\n@@ -34613,14 +34616,15 @@\n \"294241\": 55,\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+ \"29751739\": 2461,\n \"298\": [2300, 2666],\n \"2982\": 2614,\n \"2983\": 2614,\n \"2984\": 2614,\n \"2985\": 2614,\n \"2988071523335984\": 1114,\n \"299\": 2666,\n@@ -34736,15 +34740,15 @@\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- \"34\": [12, 28, 144, 441, 1880, 1919, 2208, 2463, 2491, 2566, 2583, 2641, 2657, 2666],\n+ \"34\": [12, 28, 144, 441, 1880, 1919, 2208, 2461, 2463, 2491, 2566, 2583, 2641, 2657, 2666],\n \"340\": [2238, 2576],\n \"34132519\": [680, 2659],\n \"3421\": 2615,\n \"343\": 2666,\n \"34317802\": 1153,\n \"34376245\": 2635,\n \"3456\": 13,\n@@ -34763,15 +34767,15 @@\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+ \"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@@ -34807,26 +34811,26 @@\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, 2463, 2641, 2657],\n+ \"39\": [30, 58, 2208, 2461, 2463, 2641, 2657],\n \"390\": [2270, 2300],\n \"3900\": 2615,\n \"3900x\": 2463,\n \"39015\": 2316,\n- \"39091772\": 2461,\n \"39211752\": 1153,\n \"39337286e\": 1149,\n \"3971\": 2615,\n \"39804426\": 1153,\n \"3992\": 2615,\n \"39924804\": [2339, 2352, 2382, 2389, 2399, 2429, 2436, 2449],\n+ \"3995521\": 2488,\n \"3_000\": 669,\n \"3abcd\": 513,\n \"3d\": [63, 2513, 2621, 2635, 2637, 2657, 2666],\n \"3e\": [357, 359, 1596, 1653, 1710, 1767, 1824, 1879, 1893, 1915, 2086],\n \"3ej\": 2086,\n \"3int8\": 2645,\n \"3j\": [58, 374, 544, 647, 1157, 2108, 2572],\n@@ -34879,15 +34883,15 @@\n \"4167\": 1643,\n \"4170\": 2617,\n \"4176\": 2617,\n \"4181\": [28, 2621],\n \"4187\": 2617,\n \"4191\": 2617,\n \"4197\": 2617,\n- \"42\": [31, 58, 63, 147, 349, 669, 896, 897, 974, 1029, 2090, 2208, 2256, 2332, 2376, 2423, 2457, 2461, 2566, 2605, 2622, 2635, 2639, 2657, 2664, 2665, 2666],\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 \"423\": 55,\n@@ -34903,30 +34907,29 @@\n \"42667924\": 1154,\n \"4267\": 2617,\n \"4270\": 2617,\n \"4276\": 2617,\n \"429\": 136,\n \"4294967293\": 2639,\n \"4294967296\": [196, 836, 1008, 1179, 1266, 1421, 1940],\n- \"43\": [2208, 2583, 2635, 2641, 2657, 2666],\n+ \"43\": [2208, 2461, 2583, 2635, 2641, 2657, 2666],\n \"430148\": 2635,\n \"43014843\": 2635,\n \"43181166\": 2458,\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- \"44079942\": 2461,\n \"4408\": 2617,\n \"44089210e\": 1527,\n \"4408921e\": [1765, 2175],\n \"4409e\": 2091,\n \"442\": 2615,\n \"4428\": 2617,\n \"4434142\": 349,\n@@ -34953,15 +34956,15 @@\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@@ -35127,22 +35130,20 @@\n \"54959369\": 2666,\n \"54999924\": 1247,\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- \"55215758\": 2488,\n \"5524\": 2621,\n \"55458479\": 349,\n \"55490914e\": 2666,\n \"5555555555555554\": 1349,\n \"55627469\": 349,\n \"55645993\": 2635,\n- \"55792744\": 2461,\n \"5580\": 2535,\n \"55914881e\": 2104,\n \"56\": [52, 55, 61, 544, 1764, 2204, 2463, 2657, 2659],\n \"5612\": 2621,\n \"5614\": 2522,\n \"562\": [680, 2659],\n \"5620499351813308\": 86,\n@@ -35160,14 +35161,15 @@\n \"57136612e\": 2173,\n \"57510612\": 660,\n \"576\": 2615,\n \"57721\": [2326, 2371, 2418],\n \"5772156649015328606065120900824024310421\": 76,\n \"5773\": 2522,\n \"57860025\": 1154,\n+ \"57921891\": 2461,\n \"579365079365115\": [1113, 1543],\n \"57x\": 2594,\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@@ -35270,14 +35272,15 @@\n \"6526\": 2522,\n \"6527\": 2522,\n \"6530\": 2522,\n \"6532\": 2522,\n \"6536\": 2522,\n \"6537\": 2522,\n \"6538\": 2522,\n+ \"65387438\": 2488,\n \"6546\": 2522,\n \"65465\": [2335, 2378, 2425],\n \"6551\": 2525,\n \"65522\": [142, 546],\n \"6553\": 2522,\n \"65535\": [584, 2619, 2622],\n \"6556\": 2522,\n@@ -35364,15 +35367,15 @@\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- \"69\": [58, 431, 2461, 2657, 2666],\n+ \"69\": [58, 431, 2657, 2666],\n \"6916\": 2524,\n \"6922\": 2524,\n \"6924\": 2524,\n \"69312169\": [1113, 1543],\n \"69314718\": [76, 657, 2655],\n \"69314718055994529\": 657,\n \"6931471805599453\": 2257,\n@@ -35427,15 +35430,14 @@\n \"729\": 2666,\n \"72904971\": 1153,\n \"72949656\": 2635,\n \"73\": [2463, 2657],\n \"7320508075688772j\": 59,\n \"73472348e\": 1816,\n \"73496154e\": 1867,\n- \"73517242\": 2488,\n \"73603959e\": 2666,\n \"73799541\": 1153,\n \"74\": [2463, 2513, 2514, 2657],\n \"74000000\": 2635,\n \"7416573867739413\": 653,\n \"74165739\": 653,\n \"74499359e\": [420, 947],\n@@ -35498,15 +35500,14 @@\n \"7755575615628914e\": 2648,\n \"77555756e\": 1877,\n \"77598074\": 349,\n \"77714685\": 349,\n \"7774613834041182\": 2315,\n \"7776\": [99, 906],\n \"7778\": 2527,\n- \"7786327\": 2461,\n \"7793\": 2527,\n \"78\": [2091, 2644, 2657],\n \"78096262\": [2352, 2399, 2449],\n \"7816\": 2527,\n \"7821\": 2527,\n \"7824\": 2527,\n \"7835\": 2527,\n@@ -35533,15 +35534,14 @@\n \"7939\": 2527,\n \"79479508\": [2345, 2391, 2439],\n \"795\": 650,\n \"7953\": 2527,\n \"7954\": 2527,\n \"7955\": 2527,\n \"79579319e\": 1867,\n- \"796\": 2461,\n \"79694221e\": 1586,\n \"7972\": 2527,\n \"7976931348623157e\": 1335,\n \"79769313e\": 1335,\n \"79ff\": [102, 125],\n \"7e\": 669,\n \"7e13\": 55,\n@@ -35564,16 +35564,14 @@\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- \"81698516\": 2488,\n- \"81716537\": 2461,\n \"81814867\": [2339, 2352, 2382, 2389, 2399, 2429, 2436, 2449],\n \"8192\": [72, 517, 2092, 2619],\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@@ -35582,15 +35580,14 @@\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- \"83003832\": 2488,\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@@ -35604,14 +35601,15 @@\n \"84147098j\": 2666,\n \"841471\": 2642,\n \"842523\": 2515,\n \"84680802e\": 2104,\n \"8480354764257312\": 653,\n \"85\": [409, 2657],\n \"85099543\": 1822,\n+ \"851\": 2461,\n \"85355339\": 1756,\n \"85569\": 2098,\n \"85602287\": [2335, 2378, 2425],\n \"857\": 410,\n \"8570331885190563e\": [648, 653],\n \"85715698e\": 2171,\n \"8577\": 2539,\n@@ -35621,17 +35619,19 @@\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+ \"86732915\": 2461,\n \"86820401\": [2345, 2391, 2439],\n \"86864911e\": 1586,\n \"87\": [2616, 2657],\n+ \"87415296\": 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@@ -35668,15 +35668,15 @@\n \"90476190e\": 1816,\n \"90909091\": 136,\n \"909297\": 2642,\n \"90929743\": 2666,\n \"91\": 2657,\n \"91275558\": 2635,\n \"916666666666666\": 1240,\n- \"92\": [98, 2461, 2657, 2659],\n+ \"92\": [98, 2657, 2659],\n \"921fb54442d18p\": 2520,\n \"9223372036854775807\": 2648,\n \"9223372036854775808\": 2648,\n \"92346708\": 349,\n \"92362781e\": 2104,\n \"92387953\": 642,\n \"92387953j\": 642,\n@@ -35704,15 +35704,14 @@\n \"9373\": 2532,\n \"9374\": 2532,\n \"9376\": 2532,\n \"9377\": 2532,\n \"93773029\": 349,\n \"9378\": 2532,\n \"9379\": 2532,\n- \"939\": 2461,\n \"9390\": [2533, 2534],\n \"94\": [409, 669, 2635, 2657],\n \"940\": 2587,\n \"941257\": 2635,\n \"94125714\": 2635,\n \"94708397920832\": 2642,\n \"9475673279178444\": 2348,\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- \"98353266\": 2461,\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@@ -35789,14 +35787,15 @@\n \"9902\": 2666,\n \"990278\": 2635,\n \"99027828\": 2635,\n \"99060736\": 2666,\n \"99091858\": [2345, 2391, 2439],\n \"99149989\": [2345, 2391, 2439],\n \"9917\": 2343,\n+ \"9917921\": 2461,\n \"99256089\": 349,\n \"99322285\": [88, 101],\n \"99394529\": [2339, 2352, 2382, 2389, 2399, 2429, 2436, 2449],\n \"99417356\": 1754,\n \"99507202\": 349,\n \"99734545\": 1154,\n \"998\": 2535,\n"}]}]}]}]}]}