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-4.13 ms +- 80.6 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-6.18 ms +- 25.9 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+10.9 ms +- 2.19 ms per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+19.9 ms +- 2.7 ms 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-3.45 ms +- 30.1 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-5.83 ms +- 19 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+9.95 ms +- 2.14 ms per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+26.7 ms +- 5.02 ms 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-12.1 ms +- 28.8 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-14.1 ms +- 11.3 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+39.8 ms +- 3.06 ms per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+43.1 ms +- 5.54 ms 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([0.10251134, 0.85299618, 0.56613854])\n+Out[7]: array([0.3128215 , 0.78171961, 0.38668424])\n \n In [8]: rng.random(3, dtype=np.float32)\n-Out[8]: array([0.00238842, 0.97557807, 0.6222447 ], dtype=float32)\n+Out[8]: array([0.9865558, 0.8202648, 0.9328461], dtype=float32)\n \n In [9]: rng.integers(0, 256, size=3, dtype=np.uint8)\n-Out[9]: array([ 94, 222, 12], dtype=uint8)\n+Out[9]: array([ 23, 124, 136], 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([0.29345037, 0.5070472 ])\n+Out[12]: array([0.85854782, 0.01759267])\n \n In [13]: print(existing)\n-[0.29345037 0.5070472 0. 0. ]\n+[0.85854782 0.01759267 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([1.21829748, 0.00137394])\n+Out[4]: array([0.9661763 , 0.31407588])\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([5.4837126 , 5.48233866], domain=[0., 9.], window=[-1., 1.], symbol='x')\n+Out[6]: Polynomial([4.66186924, 4.34779336], 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([0.00137394, 1.21829748], domain=[-1., 1.], window=[-1., 1.], symbol='x')\n+Out[7]: Polynomial([0.31407588, 0.9661763 ], 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([1.21829748, 0.00137394])\n+Out[4]: array([0.9661763 , 0.31407588])\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([5.4837126 , 5.48233866], domain=[0., 9.], window=[-1.,\n+Out[6]: Polynomial([4.66186924, 4.34779336], 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([0.00137394, 1.21829748], domain=[-1., 1.], window=[-1.,\n+Out[7]: Polynomial([0.31407588, 0.9661763 ], 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": "@@ -32317,19 +32317,17 @@\n \"0003163943736596009\": 2315,\n \"00032805\": 1697,\n \"000e\": [410, 2657],\n \"000j\": 1335,\n \"001\": [335, 420, 947, 1541, 1596, 1602, 1653, 1659, 1710, 1716, 1767, 1773, 1824, 1830, 1879, 1886, 1893, 2160],\n \"0010\": 1519,\n \"0011\": 138,\n- \"00137394\": 2488,\n \"001637457145670096\": 2315,\n \"001j\": [1596, 1653, 1710, 1767, 1824, 1879, 1893],\n \"002\": [1335, 1602, 1659, 1716, 1773, 1830, 1886],\n- \"00238842\": 2461,\n \"0024\": 477,\n \"003\": [2327, 2372, 2419],\n \"005\": 2188,\n \"0050000029\": [357, 359],\n \"0050045159\": [357, 359],\n \"00578369\": 1754,\n \"00625\": 1585,\n@@ -32346,21 +32344,22 @@\n \"012\": [1602, 1659, 1716, 1773, 1830, 1886],\n \"0123456789\": [303, 2132],\n \"01280782\": [2335, 2378, 2425],\n \"016\": [648, 653],\n \"01652764\": 2634,\n \"01666667\": 1544,\n \"016j\": 2105,\n+ \"01759267\": 2461,\n \"01831564\": 1660,\n \"018318\": [2353, 2400, 2450],\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+ \"02\": [54, 55, 147, 162, 163, 410, 547, 566, 669, 1335, 1586, 1601, 1658, 1715, 1772, 1816, 1829, 1885, 2104, 2461],\n \"020995\": 57,\n \"02284196\": 1697,\n \"02294967\": 1640,\n \"023\": 2643,\n \"02332573e\": 54,\n \"0253\": 2651,\n \"02654825\": 1891,\n@@ -32389,15 +32388,15 @@\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+ \"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@@ -32501,15 +32500,14 @@\n \"10100\": [143, 570],\n \"1015\": 2592,\n \"10151\": 2560,\n \"102\": [2463, 2636, 2665],\n \"1023\": [141, 2583],\n \"1024\": [66, 72, 2657],\n \"10240\": 977,\n- \"10251134\": 2461,\n \"103\": 2463,\n \"10330\": 55,\n \"10339\": [2536, 2542],\n \"1035\": [1643, 1655],\n \"10352\": 2542,\n \"10368\": 2536,\n \"10375\": 2536,\n@@ -32714,15 +32712,15 @@\n \"12345678903141592653589793\": 2299,\n \"123456789a12\": 25,\n \"123456789a123456789b\": 25,\n \"1234567e\": 2172,\n \"12346\": 2462,\n \"1235\": 2091,\n \"123abc\": [302, 305, 2131, 2134],\n- \"124\": [98, 905],\n+ \"124\": [98, 905, 2461],\n \"125\": [470, 660, 1114, 1142, 1645, 1651, 1899, 1900, 2239, 2339, 2382, 2429, 2460, 2491, 2658, 2665],\n \"12589991e\": 645,\n \"126\": [863, 1048, 1116, 1904],\n \"1261\": 2612,\n \"12658\": 2560,\n \"12697628\": 2634,\n \"127\": [62, 66, 514, 863, 1048, 1102, 1116, 1904, 2301, 2302, 2462, 2463, 2464, 2583, 2638],\n@@ -32775,14 +32773,15 @@\n \"13561\": 2551,\n \"13562\": 2551,\n \"13563\": 2551,\n \"13564\": 2551,\n \"13565\": 2551,\n \"13578\": 2576,\n \"13587\": 2551,\n+ \"136\": 2461,\n \"13605\": 2560,\n \"13610\": 2560,\n \"13620\": 2551,\n \"13641\": 2551,\n \"13644\": 2551,\n \"1366\": 36,\n \"13698\": 2560,\n@@ -33732,15 +33731,14 @@\n \"21623\": [2588, 2594],\n \"21627\": 2594,\n \"21645\": 2594,\n \"21663\": 2588,\n \"21760\": 2622,\n \"218\": [566, 2463],\n \"21807\": 2594,\n- \"21829748\": 2488,\n \"2184\": 2225,\n \"21866\": 2589,\n \"21867\": 2589,\n \"21868\": 2589,\n \"21869\": 2589,\n \"21870\": 2589,\n \"219\": 2463,\n@@ -33777,15 +33775,15 @@\n \"22137\": 2599,\n \"22139\": 2594,\n \"22148\": 2591,\n \"22155\": 2591,\n \"22156\": 2591,\n \"22159\": 2594,\n \"22195\": 2591,\n- \"222\": [642, 669, 2460, 2461],\n+ \"222\": [642, 669, 2460],\n \"22214\": 2591,\n \"22215\": 2591,\n \"22216\": 2591,\n \"22220\": 2591,\n \"22221\": 2591,\n \"22222\": 2591,\n \"222222\": 1335,\n@@ -33894,15 +33892,15 @@\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, 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, 2461, 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@@ -34171,15 +34169,15 @@\n \"2495\": 2615,\n \"24955\": 2604,\n \"24962\": 2604,\n \"24971\": 2604,\n \"24972\": 2604,\n \"24977\": 2604,\n \"24978\": 2622,\n- \"25\": [10, 50, 54, 55, 56, 58, 69, 140, 361, 377, 409, 418, 440, 481, 489, 520, 526, 528, 544, 624, 645, 660, 667, 669, 680, 870, 881, 893, 917, 1056, 1070, 1083, 1135, 1142, 1143, 1240, 1349, 1526, 1527, 1542, 1581, 1606, 1651, 1694, 1702, 1834, 1907, 2089, 2090, 2091, 2204, 2239, 2240, 2251, 2265, 2266, 2323, 2325, 2337, 2348, 2349, 2367, 2380, 2390, 2396, 2414, 2427, 2438, 2446, 2461, 2463, 2473, 2476, 2491, 2513, 2515, 2519, 2567, 2602, 2604, 2622, 2623, 2634, 2640, 2644, 2653, 2656, 2658, 2665],\n+ \"25\": [10, 50, 54, 55, 56, 58, 69, 140, 361, 377, 409, 418, 440, 481, 489, 520, 526, 528, 544, 624, 645, 660, 667, 669, 680, 870, 881, 893, 917, 1056, 1070, 1083, 1135, 1142, 1143, 1240, 1349, 1526, 1527, 1542, 1581, 1606, 1651, 1694, 1702, 1834, 1907, 2089, 2090, 2091, 2204, 2239, 2240, 2251, 2265, 2266, 2323, 2325, 2337, 2348, 2349, 2367, 2380, 2390, 2396, 2414, 2427, 2438, 2446, 2463, 2473, 2476, 2491, 2513, 2515, 2519, 2567, 2602, 2604, 2622, 2623, 2634, 2640, 2644, 2653, 2656, 2658, 2665],\n \"250\": [361, 2463],\n \"2500\": 652,\n \"25000\": 652,\n \"25003\": 2604,\n \"25043\": 2604,\n \"25049\": 2604,\n \"25054\": 2622,\n@@ -34327,15 +34325,15 @@\n \"25914\": 2622,\n \"25943\": 2622,\n \"25954\": 2622,\n \"25d0\": 32,\n \"25j\": 2658,\n \"25t03\": 55,\n \"25x\": 138,\n- \"26\": [29, 30, 40, 50, 54, 55, 58, 63, 79, 146, 944, 2204, 2208, 2310, 2333, 2377, 2424, 2513, 2519, 2534, 2536, 2537, 2577, 2599, 2601, 2622, 2625, 2629, 2640, 2656, 2657, 2665],\n+ \"26\": [29, 30, 40, 50, 54, 55, 58, 63, 79, 146, 944, 2204, 2208, 2310, 2333, 2377, 2424, 2461, 2513, 2519, 2534, 2536, 2537, 2577, 2599, 2601, 2622, 2625, 2629, 2640, 2656, 2657, 2665],\n \"260\": [162, 1328, 2238, 2576, 2665],\n \"26064346e\": 147,\n \"26081\": 2625,\n \"26103\": 2625,\n \"26137788e\": 2104,\n \"26157\": 2625,\n \"262\": 2665,\n@@ -34506,15 +34504,15 @@\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, 2640, 2648, 2656, 2658, 2665],\n+ \"28\": [36, 54, 55, 146, 409, 661, 1695, 1704, 1707, 1862, 2168, 2208, 2225, 2463, 2513, 2538, 2539, 2540, 2543, 2629, 2640, 2648, 2656, 2658, 2665],\n \"28000000e\": 1335,\n \"2800000e\": 1335,\n \"28006\": 2630,\n \"28007\": 2630,\n \"2801\": 2613,\n \"28021\": 2630,\n \"28044\": 2630,\n@@ -34578,15 +34576,14 @@\n \"290\": 2300,\n \"29001ed\": 13,\n \"290301\": 55,\n \"292\": 55,\n \"29229249\": 524,\n \"29239766\": 54,\n \"2925464970228\": 657,\n- \"29345037\": 2461,\n \"294241\": 55,\n \"296\": 669,\n \"2969\": 2614,\n \"297\": [438, 2477, 2665],\n \"29718677\": [2339, 2352, 2382, 2389, 2399, 2429, 2436, 2449],\n \"2973\": 2614,\n \"29737120e\": 566,\n@@ -34622,15 +34619,15 @@\n \"2nd\": [513, 641, 642, 655, 658, 669, 1526, 2335, 2378, 2425, 2636, 2640, 2665],\n \"2to3\": 2616,\n \"2x\": [1527, 1542, 2357, 2404, 2454, 2488, 2491, 2616, 2619],\n \"2x2\": 47,\n \"2x3\": [47, 72, 2664],\n \"2x3x5\": 336,\n \"3\": [1, 2, 5, 10, 11, 12, 14, 20, 24, 26, 29, 30, 31, 32, 34, 36, 37, 38, 42, 47, 50, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 66, 70, 72, 74, 76, 78, 79, 87, 89, 94, 96, 97, 98, 99, 100, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119, 120, 121, 123, 124, 127, 128, 130, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 167, 169, 171, 176, 177, 185, 186, 194, 196, 204, 210, 213, 214, 227, 229, 234, 238, 239, 251, 260, 261, 262, 263, 264, 270, 278, 280, 284, 287, 290, 312, 316, 318, 322, 323, 333, 335, 336, 337, 338, 340, 341, 342, 345, 346, 347, 348, 349, 350, 351, 353, 354, 355, 356, 357, 358, 359, 362, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 396, 398, 401, 404, 408, 409, 410, 416, 417, 420, 421, 422, 423, 432, 435, 436, 440, 441, 442, 443, 447, 448, 450, 451, 454, 456, 460, 461, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 480, 482, 483, 487, 488, 513, 514, 516, 518, 519, 520, 523, 524, 526, 527, 528, 529, 530, 531, 532, 533, 534, 538, 540, 541, 542, 543, 544, 545, 547, 549, 550, 553, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 573, 574, 575, 582, 592, 596, 602, 608, 622, 623, 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54, 55, 57, 58, 63, 263, 336, 355, 360, 363, 409, 454, 484, 533, 864, 875, 977, 1049, 1064, 1113, 1117, 1118, 1225, 1308, 1462, 1543, 1638, 1906, 1911, 1982, 2089, 2103, 2115, 2165, 2204, 2216, 2224, 2241, 2316, 2319, 2322, 2323, 2325, 2326, 2329, 2339, 2340, 2344, 2371, 2373, 2382, 2383, 2386, 2394, 2418, 2420, 2429, 2430, 2433, 2444, 2463, 2513, 2531, 2587, 2608, 2636, 2640, 2644, 2656, 2665],\n \"300\": [66, 363, 2238, 2576, 2644],\n \"3000\": 2594,\n \"30000\": 533,\n \"3000488281\": 476,\n \"3003003\": 1999,\n \"3006\": 2614,\n \"3007\": 2614,\n@@ -34656,20 +34653,22 @@\n \"3117\": 2614,\n \"3118\": [57, 2547],\n \"31183145\": 2665,\n \"312088\": 1867,\n \"3124\": 2614,\n \"3125\": 2081,\n \"3128\": 2614,\n+ \"3128215\": 2461,\n \"313\": 2665,\n \"3131\": 2614,\n \"3134\": 2614,\n \"3135\": 2614,\n \"3136\": 2614,\n \"314\": [420, 947],\n+ \"31407588\": 2488,\n \"3141\": 562,\n \"3153\": 2615,\n \"31534378e\": 660,\n \"316\": [680, 1923, 2658],\n \"3160\": 2615,\n \"3168\": 2615,\n \"3173\": 2617,\n@@ -34721,14 +34720,15 @@\n \"34317802\": 1153,\n \"34376245\": 2634,\n \"3456\": 13,\n \"3458\": 2615,\n \"3471280\": 1923,\n \"3472\": 2615,\n \"34732142857143039\": [1113, 1543],\n+ \"34779336\": 2488,\n \"347845\": 2634,\n \"34784527\": 2634,\n \"3480\": 2615,\n \"3484692283495345\": [648, 653],\n \"34889999999999999\": [2325, 2369, 2416],\n \"34890909\": 523,\n \"34960421\": 680,\n@@ -34772,23 +34772,24 @@\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+ \"38668424\": 2461,\n \"38672696\": [2352, 2399, 2449],\n \"3871\": 2615,\n \"38777878e\": [147, 1651],\n \"38791518e\": [421, 948],\n \"38885\": [2361, 2408],\n \"389056\": 2641,\n \"3890561\": [38, 2665],\n \"3891\": 2641,\n- \"39\": [30, 58, 2208, 2463, 2640, 2656],\n+ \"39\": [30, 58, 2208, 2461, 2463, 2640, 2656],\n \"390\": [2270, 2300],\n \"3900\": 2615,\n \"3900x\": 2463,\n \"39015\": 2316,\n \"39211752\": 1153,\n \"39337286e\": 1149,\n \"3971\": 2615,\n@@ -34875,15 +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, 2583, 2634, 2640, 2656, 2665],\n+ \"43\": [2208, 2461, 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@@ -34910,15 +34911,15 @@\n \"4476\": 2621,\n \"4483\": 2617,\n \"4485\": 2617,\n \"4486\": 2617,\n \"449294e\": 2170,\n \"44948974\": 2658,\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, 2636, 2643, 2656, 2665],\n+ \"45\": [12, 18, 38, 58, 94, 105, 130, 339, 666, 851, 866, 944, 1025, 1026, 1031, 1051, 1212, 1882, 1886, 2103, 2204, 2636, 2643, 2656, 2665],\n \"450\": 55,\n \"45000005\": 2115,\n \"45038594\": [349, 2638],\n \"45053314\": 2634,\n \"4511316\": 2665,\n \"4520525295346629\": 1228,\n \"4532\": [409, 661, 2168],\n@@ -34968,17 +34969,15 @@\n \"48\": [58, 270, 355, 880, 1069, 1142, 1229, 1312, 1466, 1867, 1986, 2208, 2239, 2323, 2367, 2414, 2656, 2658],\n \"480\": [238, 858, 1041, 1207, 1290, 1444, 1964],\n \"4800\": 57,\n \"48000000\": 2634,\n \"4809319\": 1153,\n \"4816\": [99, 906],\n \"48219694e\": [421, 948],\n- \"48233866\": 2488,\n \"4836\": 2618,\n- \"4837126\": 2488,\n \"484\": [2517, 2583, 2625],\n \"4853\": 2618,\n \"4861946401452\": 2334,\n \"4874\": [409, 661, 2168],\n \"4882\": [287, 1241, 1324, 1478, 1998],\n \"4896\": 2620,\n \"49\": [71, 2208, 2323, 2367, 2414, 2567, 2568, 2640, 2656, 2665],\n@@ -35022,15 +35021,14 @@\n \"5047328775385895\": 2315,\n \"50491112870\": 55,\n \"50491123200\": 55,\n \"50491123200000000\": 55,\n \"50629471\": 1154,\n \"5063\": 2620,\n \"5067\": 2620,\n- \"5070472\": 2461,\n \"5082\": 2620,\n \"5095\": 2620,\n \"51\": [58, 520, 1654, 1752, 1761, 1867, 1870, 2083, 2204, 2331, 2339, 2356, 2375, 2382, 2403, 2422, 2429, 2453, 2622, 2656, 2665],\n \"510\": [143, 570],\n \"5100\": 2620,\n \"5104\": 2620,\n \"51182162\": 2665,\n@@ -35077,15 +35075,15 @@\n \"536870910\": 1902,\n \"5374\": 2621,\n \"53814331\": 2665,\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, 2641, 2656],\n+ \"54\": [38, 59, 523, 1638, 1711, 1764, 2208, 2461, 2641, 2656],\n \"540\": [2238, 2576],\n \"54030231\": 2665,\n \"54030231j\": 2665,\n \"541\": 2463,\n \"54117\": 1644,\n \"5424\": 2621,\n \"54323428\": [2345, 2391, 2439],\n@@ -35117,15 +35115,14 @@\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- \"56613854\": 2461,\n \"567\": 2643,\n \"56826729e\": 2104,\n \"56917101\": 2634,\n \"57\": [58, 669, 2204, 2322, 2366, 2413, 2463, 2491, 2636, 2656],\n \"5707963267948966\": [102, 125],\n \"57079633\": [94, 105, 130, 1911, 2238, 2665],\n \"5708\": [412, 618],\n@@ -35185,15 +35182,14 @@\n \"61799388\": 1911,\n \"618\": 669,\n \"6180\": [2353, 2400, 2450],\n \"61988120985\": [2323, 2367, 2414],\n \"61c54bbd\": 42,\n \"62\": [542, 968, 969, 2323, 2333, 2367, 2377, 2414, 2424, 2656],\n \"6208\": 2522,\n- \"6222447\": 2461,\n \"6227766\": 514,\n \"623\": [2394, 2444],\n \"62318272\": [2319, 2363, 2410],\n \"62341325\": 514,\n \"62374854\": 2665,\n \"624\": [2300, 2370, 2394, 2417, 2444, 2462],\n \"625\": [99, 478, 645, 906, 2390, 2438],\n@@ -35280,14 +35276,15 @@\n \"66\": [13, 58, 1922, 2547, 2656, 2665],\n \"6600475\": 1149,\n \"6602\": 2522,\n \"6606\": 2522,\n \"6611\": 2522,\n \"6614\": 2522,\n \"6618\": 2522,\n+ \"66186924\": 2488,\n \"6621\": 2522,\n \"6628\": 2522,\n \"6636\": 2522,\n \"6641\": 2522,\n \"6642\": 2522,\n \"6643\": 2522,\n \"66519143\": 1911,\n@@ -35475,14 +35472,15 @@\n \"7774613834041182\": 2315,\n \"7776\": [99, 906],\n \"7778\": 2527,\n \"7793\": 2527,\n \"78\": [2091, 2643, 2656],\n \"78096262\": [2352, 2399, 2449],\n \"7816\": 2527,\n+ \"78171961\": 2461,\n \"7821\": 2527,\n \"7824\": 2527,\n \"7835\": 2527,\n \"784\": 2463,\n \"7847\": 2527,\n \"784728999999999\": 1114,\n \"7849\": 2527,\n@@ -35515,15 +35513,15 @@\n \"79769313e\": 1335,\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, 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2638, 2640, 2641, 2643, 2644, 2645, 2647, 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, 2461, 2588, 2622, 2647, 2648, 2656],\n+ \"80\": [69, 396, 409, 446, 977, 2248, 2346, 2357, 2383, 2392, 2404, 2430, 2441, 2454, 2588, 2622, 2647, 2648, 2656],\n \"800\": [2335, 2378, 2425],\n \"8000\": [2350, 2352, 2397, 2399, 2447, 2449],\n \"80000000000000204\": [1113, 1543],\n \"8005\": 2527,\n \"801\": [941, 1114, 1123, 1124, 1131],\n \"8010\": 2527,\n \"8020\": 2527,\n@@ -35538,27 +35536,28 @@\n \"812997\": 2634,\n \"813\": [270, 880, 1069, 1229, 1312, 1466, 1986],\n \"81327024\": 2634,\n \"81349206\": [1113, 1543],\n \"81814867\": [2339, 2352, 2382, 2389, 2399, 2429, 2436, 2449],\n \"8192\": [72, 517, 2092, 2619],\n \"82\": [1650, 2323, 2367, 2414, 2463, 2656, 2665],\n+ \"8202648\": 2461,\n \"8207540608310198\": [2353, 2400, 2450],\n \"82276161\": 349,\n \"8230\": [2353, 2400, 2450],\n \"82485143\": 2634,\n \"82502011\": 349,\n \"8255\": 2566,\n \"826716f\": 2521,\n \"82743037\": 524,\n \"82770259\": 2665,\n \"8277025938204418\": 2665,\n \"827941\": [514, 680, 2658],\n \"82842712\": [642, 644],\n- \"83\": [2105, 2167, 2353, 2400, 2450, 2461, 2554, 2656],\n+ \"83\": [2105, 2167, 2353, 2400, 2450, 2554, 2656],\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@@ -35572,22 +35571,22 @@\n \"84147098j\": 2665,\n \"841471\": 2641,\n \"842523\": 2515,\n \"84680802e\": 2104,\n \"8480354764257312\": 653,\n \"85\": [409, 2656],\n \"85099543\": 1822,\n- \"85299618\": 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+ \"85854782\": 2461,\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 \"8601\": [55, 62, 67, 2613],\n \"86260211e\": 54,\n \"8630830\": 13,\n \"86399\": 55,\n@@ -35660,51 +35659,53 @@\n \"92771843\": 1154,\n \"9299\": 2532,\n \"93\": 2656,\n \"9304e\": 2091,\n \"931\": 2587,\n \"9317\": 2532,\n \"9319\": 2532,\n+ \"9328461\": 2461,\n \"9339\": 2532,\n \"9340\": 2532,\n \"934284\": 349,\n \"93657855\": 349,\n \"9371\": 2532,\n \"9372\": 2532,\n \"9373\": 2532,\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, 2461, 2634, 2656],\n+ \"94\": [409, 669, 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- \"95\": [37, 39, 646, 2353, 2400, 2450, 2634, 2653, 2656],\n+ \"95\": [37, 39, 646, 2353, 2400, 2450, 2461, 2634, 2653, 2656],\n \"9504637\": 2665,\n \"950684\": 2634,\n \"95068423\": 2634,\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\": 2665,\n \"96\": [62, 69, 1577, 1867, 2303, 2463, 2566, 2647, 2656, 2658, 2667],\n \"96139749\": 2665,\n \"96202397\": [2335, 2378, 2425],\n \"96360618\": [2387, 2434],\n+ \"9661763\": 2488,\n \"9665554\": 349,\n \"96767474e\": 54,\n \"96875\": 2491,\n \"96979195\": 2634,\n \"969792\": 2634,\n \"96e7\": 42,\n \"97\": [2463, 2634, 2656, 2665],\n@@ -35717,15 +35718,14 @@\n \"9736\": [2533, 2534],\n \"9742\": [2533, 2534],\n \"9744\": [2533, 2534],\n \"9745\": [2533, 2534],\n \"9746\": [2533, 2534],\n \"9747\": [2533, 2534],\n \"97517215\": 349,\n- \"97557807\": 2461,\n \"97562235\": [349, 2457, 2638],\n \"9757\": [2533, 2534],\n \"9764\": [2533, 2534],\n \"9765\": [2533, 2534],\n \"9766\": [2533, 2534],\n \"9767\": [2533, 2534],\n \"9771\": [2533, 2534],\n@@ -35740,14 +35740,15 @@\n \"9800\": 2665,\n \"9801\": 2665,\n \"9802\": 2665,\n \"98024613\": 680,\n \"9807642\": 1153,\n \"981\": 2592,\n \"98136677\": 523,\n+ \"9865558\": 2461,\n \"987\": 28,\n \"987654321\": 2393,\n \"98935825\": 2665,\n \"9897\": 2665,\n \"9898\": 2665,\n \"9899\": [105, 130, 2665],\n \"99\": [12, 302, 408, 544, 672, 1096, 1906, 2131, 2460, 2634, 2656, 2657, 2665],\n@@ -45945,15 +45946,15 @@\n \"typevar\": 2517,\n \"typic\": [1, 4, 5, 6, 8, 9, 10, 11, 12, 13, 19, 20, 21, 22, 36, 39, 42, 54, 55, 58, 59, 61, 63, 65, 70, 72, 74, 78, 91, 114, 159, 161, 354, 409, 422, 427, 443, 457, 521, 522, 548, 571, 572, 579, 582, 583, 627, 655, 814, 850, 1030, 1513, 1526, 1577, 1578, 1580, 1585, 1588, 1640, 1645, 1697, 1702, 1754, 1759, 1811, 1816, 1867, 2089, 2094, 2123, 2126, 2127, 2138, 2139, 2145, 2219, 2223, 2226, 2251, 2258, 2290, 2334, 2462, 2473, 2507, 2513, 2514, 2515, 2517, 2518, 2542, 2599, 2616, 2634, 2636, 2643, 2644, 2646, 2647, 2651, 2652, 2653, 2667, 2668],\n \"typo\": [13, 16, 2535, 2556, 2573, 2587, 2595, 2614, 2617],\n \"tzinfo\": [67, 360],\n \"tzoffset\": 67,\n \"t\\u2081\": 1895,\n \"t\\u2082\": 1895,\n- \"u\": [10, 11, 12, 13, 14, 16, 18, 24, 30, 40, 50, 55, 56, 57, 62, 67, 69, 74, 78, 150, 163, 270, 302, 305, 360, 397, 560, 636, 642, 644, 659, 669, 880, 1069, 1148, 1229, 1312, 1345, 1348, 1466, 1542, 1585, 1645, 1702, 1759, 1816, 1871, 1986, 2086, 2131, 2134, 2213, 2230, 2270, 2358, 2405, 2455, 2461, 2464, 2499, 2507, 2508, 2510, 2513, 2535, 2542, 2554, 2556, 2572, 2599, 2622, 2625, 2629, 2641, 2646, 2647, 2648, 2655, 2664, 2668],\n+ \"u\": [10, 11, 12, 13, 14, 16, 18, 24, 30, 40, 50, 55, 56, 57, 62, 67, 69, 74, 78, 150, 163, 270, 302, 305, 360, 397, 560, 636, 642, 644, 659, 669, 880, 1069, 1148, 1229, 1312, 1345, 1348, 1466, 1542, 1585, 1645, 1702, 1759, 1816, 1871, 1986, 2086, 2131, 2134, 2213, 2230, 2270, 2358, 2405, 2455, 2464, 2499, 2507, 2508, 2510, 2513, 2535, 2542, 2554, 2556, 2572, 2599, 2622, 2625, 2629, 2641, 2646, 2647, 2648, 2655, 2664, 2668],\n \"u0\": 2529,\n \"u1\": [56, 57, 377, 1096, 1903, 1922, 2146, 2151, 2230, 2547, 2644],\n \"u10\": [56, 1922, 2644],\n \"u11\": [2320, 2364, 2411],\n \"u12\": 669,\n \"u13\": [2469, 2503],\n \"u16\": [56, 389],\n"}]}]}]}]}]}