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Results (displaying all 30 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.396154108207169536.4	x¹⁶ - 2x¹⁴ + 2x¹² - 4x¹⁰ - 8x⁸ + 8x⁶ + 8x⁴ + 16x² + 16	$ 2^{36}\cdot 7^{8} $	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.0.531312517142544384.2	x¹⁶ - 2x¹⁵ - 4x¹⁴ + 4x¹³ + 31x¹² - 62x¹¹ + 58x¹⁰ - 96x⁹ + 141x⁸ - 96x⁷ + 58x⁶ - 62x⁵ + 31x⁴ + 4x³ - 4x² - 2x + 1	$ 2^{24}\cdot 3^{8}\cdot 13^{6} $	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.0.1943346986288676864.2	x¹⁶ + x¹⁴ - 11x¹² + 5x¹⁰ + 36x⁸ - 65x⁶ + 31x⁴ + 8x² + 1	$ 2^{20}\cdot 3^{8}\cdot 7^{10} $	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.0.5951500145509072896.3	x¹⁶ - 3x¹⁴ + 12x¹² - 27x¹⁰ + 92x⁸ - 135x⁶ + 111x⁴ - 60x² + 16	$ 2^{16}\cdot 3^{8}\cdot 7^{12} $	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.4.6871947673600000000.4	x¹⁶ - 10x¹² + 27x⁸ - 50x⁴ + 1	$ 2^{44}\cdot 5^{8} $	$C_2\wr C_2^2$ (as 16T128)	Trivial (GRH)
16.0.7465802011608416256.1	x¹⁶ + 11x¹² + 24x⁸ + 11x⁴ + 1	$ 2^{16}\cdot 3^{12}\cdot 11^{8} $	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.0.8501000274280710144.1	x¹⁶ - 4x¹⁵ + 2x¹⁴ - 2x¹³ + 24x¹² - 42x¹¹ + 100x¹⁰ - 84x⁹ - 69x⁸ + 70x⁷ + 52x⁶ - 72x⁵ + 34x⁴ - 6x³ - 6x² + 2x + 1	$ 2^{28}\cdot 3^{8}\cdot 13^{6} $	$C_2\wr C_2^2$ (as 16T128)	$[2]$
16.0.8501000274280710144.2	x¹⁶ - 6x¹⁵ + 14x¹⁴ - 22x¹³ + 42x¹² - 64x¹¹ + 48x¹⁰ - 58x⁹ + 187x⁸ - 336x⁷ + 420x⁶ - 522x⁵ + 648x⁴ - 702x³ + 594x² - 324x + 81	$ 2^{28}\cdot 3^{8}\cdot 13^{6} $	$C_2\wr C_2^2$ (as 16T128)	$[2]$
16.0.9349208943630483456.5	x¹⁶ - 10x¹² + 51x⁸ + 14x⁴ + 1	$ 2^{44}\cdot 3^{12} $	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.0.13272536909526073344.1	x¹⁶ - 4x¹⁴ + 11x¹² - 9x¹⁰ - 4x⁸ - 3x⁶ + 5x⁴ + 5x² + 1	$ 2^{20}\cdot 3^{10}\cdot 11^{8} $	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.0.16620815899787526144.3	x¹⁶ - 8x¹⁴ + 24x¹² - 8x¹¹ - 16x¹⁰ + 48x⁹ - 44x⁸ - 48x⁷ + 112x⁶ - 96x⁵ + 28x⁴ + 184x³ - 24x² - 64x + 19	$ 2^{48}\cdot 3^{10} $	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.4.20882706457600000000.1	x¹⁶ - 5x¹² - 8x⁸ - 5x⁴ + 1	$ 2^{16}\cdot 5^{8}\cdot 13^{8} $	$C_2\wr C_2^2$ (as 16T128)	Trivial (GRH)
16.0.25353862925258850304.1	x¹⁶ - 2x¹⁴ + 10x¹² + 10x¹⁰ + 26x⁸ + 10x⁶ + 10x⁴ - 2x² + 1	$ 2^{42}\cdot 7^{8} $	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.0.25353862925258850304.3	x¹⁶ - 10x¹⁴ + 34x¹² - 42x¹⁰ + 2x⁸ + 42x⁶ + 34x⁴ + 10x² + 1	$ 2^{42}\cdot 7^{8} $	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.4.51399544780206637056.2	x¹⁶ - 6x¹⁵ + 16x¹⁴ - 34x¹³ + 60x¹² - 84x¹¹ + 136x¹⁰ - 186x⁹ + 217x⁸ - 260x⁷ + 192x⁶ - 166x⁵ + 100x⁴ - 18x³ - 24x² + 12x - 3	$ 2^{24}\cdot 3^{12}\cdot 7^{8} $	$C_2\wr C_2^2$ (as 16T128)	Trivial (GRH)
16.4.91376968498145132544.1	x¹⁶ - 8x¹⁴ + 38x¹² - 116x¹⁰ + 227x⁸ - 284x⁶ + 214x⁴ - 84x² + 9	$ 2^{28}\cdot 3^{10}\cdot 7^{8} $	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.0.95224002328145166336.1	x¹⁶ - 4x¹⁵ + 6x¹³ + 35x¹² - 84x¹¹ + 101x¹⁰ - 202x⁹ + 456x⁸ - 722x⁷ + 761x⁶ - 564x⁵ + 311x⁴ - 126x³ + 39x² - 8x + 1	$ 2^{20}\cdot 3^{8}\cdot 7^{12} $	$C_2\wr C_2^2$ (as 16T128)	$[2]$
16.4.109951162777600000000.1	x¹⁶ - 4x¹⁴ - 16x¹³ - 18x¹² + 48x¹¹ + 96x¹⁰ - 16x⁹ - 149x⁸ - 80x⁷ + 48x⁶ + 72x⁵ + 22x⁴ - 8x³ - 4x² - 1	$ 2^{48}\cdot 5^{8} $	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.4.109951162777600000000.2	x¹⁶ - 4x¹⁴ + 6x¹² - 16x¹¹ - 8x¹⁰ + 24x⁹ + 15x⁸ - 80x⁷ + 208x⁶ - 256x⁵ + 194x⁴ + 8x³ - 76x² + 56x - 1	$ 2^{48}\cdot 5^{8} $	$C_2\wr C_2^2$ (as 16T128)	Trivial (GRH)
16.0.119452832185734660096.2	x¹⁶ - 7x¹⁴ + 42x¹² - 136x¹⁰ + 262x⁸ - 243x⁶ + 174x⁴ + 90x² + 9	$ 2^{20}\cdot 3^{12}\cdot 11^{8} $	$C_2\wr C_2^2$ (as 16T128)	$[2]$
16.0.149587343098087735296.7	x¹⁶ + 4x¹⁴ - 16x¹³ + 30x¹² - 48x¹¹ + 112x¹⁰ - 144x⁹ + 199x⁸ - 176x⁷ + 120x⁶ - 88x⁵ + 34x⁴ - 24x³ + 12x² + 3	$ 2^{48}\cdot 3^{12} $	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.4.822392716483306192896.1	x¹⁶ - 2x¹⁵ - 2x¹³ - 14x¹² + 6x¹¹ + 24x¹⁰ + 42x⁹ + 30x⁸ - 18x⁷ - 36x⁶ - 162x⁵ - 126x⁴ + 54x³ + 108x² + 162x + 81	$ 2^{28}\cdot 3^{12}\cdot 7^{8} $	$C_2\wr C_2^2$ (as 16T128)	$[2]$
16.8.31130283153817600000000.1	x¹⁶ - 4x¹⁵ - 8x¹⁴ + 48x¹³ + 20x¹² - 228x¹¹ - 120x¹⁰ + 514x⁹ + 877x⁸ - 812x⁷ - 2696x⁶ + 1698x⁵ + 3167x⁴ - 2266x³ - 887x² + 738x - 41	$ 2^{24}\cdot 5^{8}\cdot 41^{6} $	$C_2\wr C_2^2$ (as 16T128)	Trivial (GRH)
16.0.31130283153817600000000.2	x¹⁶ + 6x¹⁴ - 4x¹³ + 35x¹² + 8x¹¹ + 218x¹⁰ + 324x⁹ + 1031x⁸ + 1016x⁷ + 2078x⁶ + 1240x⁵ + 1681x⁴ - 152x³ + 1116x² - 1408x + 569	$ 2^{24}\cdot 5^{8}\cdot 41^{6} $	$C_2\wr C_2^2$ (as 16T128)	$[2, 2]$
16.0.31130283153817600000000.3	x¹⁶ - 2x¹⁵ + 15x¹⁴ - 42x¹³ + 109x¹² - 262x¹¹ + 460x¹⁰ - 764x⁹ + 1239x⁸ - 1510x⁷ + 2094x⁶ - 2536x⁵ + 2266x⁴ - 2532x³ + 2010x² - 868x + 961	$ 2^{24}\cdot 5^{8}\cdot 41^{6} $	$C_2\wr C_2^2$ (as 16T128)	$[4]$
16.8.189537365823025172265625.1	x¹⁶ - x¹⁵ - 8x¹⁴ - 17x¹³ - 30x¹² - 120x¹¹ - 227x¹⁰ - 72x⁹ - 46x⁸ - 167x⁷ - 342x⁶ - 300x⁵ + 205x⁴ + 148x³ - 78x² + 4x + 1	$ 5^{8}\cdot 13^{8}\cdot 29^{6} $	$C_2\wr C_2^2$ (as 16T128)	Trivial (GRH)
16.0.74743809852316057600000000.1	x¹⁶ - 4x¹⁵ + 8x¹⁴ - 8x¹³ + 36x¹² - 124x¹¹ + 260x¹⁰ - 594x⁹ + 1345x⁸ - 1460x⁷ + 3872x⁶ - 6382x⁵ + 17487x⁴ - 6326x³ + 11745x² + 10382x + 37561	$ 2^{24}\cdot 5^{8}\cdot 7^{4}\cdot 41^{6} $	$C_2\wr C_2^2$ (as 16T128)	$[2, 2, 18]$ (GRH)
16.16.74743809852316057600000000.1	x¹⁶ - 4x¹⁵ - 24x¹⁴ + 104x¹³ + 172x¹² - 876x¹¹ - 420x¹⁰ + 3082x⁹ - x⁸ - 4548x⁷ + 896x⁶ + 2246x⁵ - 217x⁴ - 362x³ + 3x² + 18x + 1	$ 2^{24}\cdot 5^{8}\cdot 7^{4}\cdot 41^{6} $	$C_2\wr C_2^2$ (as 16T128)	Trivial (GRH)
16.0.338247889767883716141015625.2	x¹⁶ - 7x¹⁵ + 33x¹⁴ - 109x¹³ + 236x¹² - 29x¹¹ - 2203x¹⁰ + 9266x⁹ - 16826x⁸ - 12945x⁷ + 186735x⁶ - 673377x⁵ + 1554248x⁴ - 2544195x³ + 2937115x² - 2197228x + 824821	$ 5^{8}\cdot 13^{8}\cdot 101^{6} $	$C_2\wr C_2^2$ (as 16T128)	$[44]$ (GRH)
16.16.620245622959489574938607616.1	x¹⁶ - 30x¹⁴ + 278x¹² - 1140x¹⁰ + 2280x⁸ - 2280x⁶ + 1112x⁴ - 240x² + 16	$ 2^{36}\cdot 3^{12}\cdot 19^{8} $	$C_2\wr C_2^2$ (as 16T128)	Trivial (GRH)

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Results (displaying all 30 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	Polynomial	Discriminant	Galois group	Class group
16.0.396154108207169536.4	x¹⁶ - 2x¹⁴ + 2x¹² - 4x¹⁰ - 8x⁸ + 8x⁶ + 8x⁴ + 16x² + 16	\( 2^{36}\cdot 7^{8} \)	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.0.531312517142544384.2	x¹⁶ - 2x¹⁵ - 4x¹⁴ + 4x¹³ + 31x¹² - 62x¹¹ + 58x¹⁰ - 96x⁹ + 141x⁸ - 96x⁷ + 58x⁶ - 62x⁵ + 31x⁴ + 4x³ - 4x² - 2x + 1	\( 2^{24}\cdot 3^{8}\cdot 13^{6} \)	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.0.1943346986288676864.2	x¹⁶ + x¹⁴ - 11x¹² + 5x¹⁰ + 36x⁸ - 65x⁶ + 31x⁴ + 8x² + 1	\( 2^{20}\cdot 3^{8}\cdot 7^{10} \)	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.0.5951500145509072896.3	x¹⁶ - 3x¹⁴ + 12x¹² - 27x¹⁰ + 92x⁸ - 135x⁶ + 111x⁴ - 60x² + 16	\( 2^{16}\cdot 3^{8}\cdot 7^{12} \)	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.4.6871947673600000000.4	x¹⁶ - 10x¹² + 27x⁸ - 50x⁴ + 1	\( 2^{44}\cdot 5^{8} \)	$C_2\wr C_2^2$ (as 16T128)	Trivial (GRH)
16.0.7465802011608416256.1	x¹⁶ + 11x¹² + 24x⁸ + 11x⁴ + 1	\( 2^{16}\cdot 3^{12}\cdot 11^{8} \)	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.0.8501000274280710144.1	x¹⁶ - 4x¹⁵ + 2x¹⁴ - 2x¹³ + 24x¹² - 42x¹¹ + 100x¹⁰ - 84x⁹ - 69x⁸ + 70x⁷ + 52x⁶ - 72x⁵ + 34x⁴ - 6x³ - 6x² + 2x + 1	\( 2^{28}\cdot 3^{8}\cdot 13^{6} \)	$C_2\wr C_2^2$ (as 16T128)	$[2]$
16.0.8501000274280710144.2	x¹⁶ - 6x¹⁵ + 14x¹⁴ - 22x¹³ + 42x¹² - 64x¹¹ + 48x¹⁰ - 58x⁹ + 187x⁸ - 336x⁷ + 420x⁶ - 522x⁵ + 648x⁴ - 702x³ + 594x² - 324x + 81	\( 2^{28}\cdot 3^{8}\cdot 13^{6} \)	$C_2\wr C_2^2$ (as 16T128)	$[2]$
16.0.9349208943630483456.5	x¹⁶ - 10x¹² + 51x⁸ + 14x⁴ + 1	\( 2^{44}\cdot 3^{12} \)	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.0.13272536909526073344.1	x¹⁶ - 4x¹⁴ + 11x¹² - 9x¹⁰ - 4x⁸ - 3x⁶ + 5x⁴ + 5x² + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{8} \)	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.0.16620815899787526144.3	x¹⁶ - 8x¹⁴ + 24x¹² - 8x¹¹ - 16x¹⁰ + 48x⁹ - 44x⁸ - 48x⁷ + 112x⁶ - 96x⁵ + 28x⁴ + 184x³ - 24x² - 64x + 19	\( 2^{48}\cdot 3^{10} \)	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.4.20882706457600000000.1	x¹⁶ - 5x¹² - 8x⁸ - 5x⁴ + 1	\( 2^{16}\cdot 5^{8}\cdot 13^{8} \)	$C_2\wr C_2^2$ (as 16T128)	Trivial (GRH)
16.0.25353862925258850304.1	x¹⁶ - 2x¹⁴ + 10x¹² + 10x¹⁰ + 26x⁸ + 10x⁶ + 10x⁴ - 2x² + 1	\( 2^{42}\cdot 7^{8} \)	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.0.25353862925258850304.3	x¹⁶ - 10x¹⁴ + 34x¹² - 42x¹⁰ + 2x⁸ + 42x⁶ + 34x⁴ + 10x² + 1	\( 2^{42}\cdot 7^{8} \)	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.4.51399544780206637056.2	x¹⁶ - 6x¹⁵ + 16x¹⁴ - 34x¹³ + 60x¹² - 84x¹¹ + 136x¹⁰ - 186x⁹ + 217x⁸ - 260x⁷ + 192x⁶ - 166x⁵ + 100x⁴ - 18x³ - 24x² + 12x - 3	\( 2^{24}\cdot 3^{12}\cdot 7^{8} \)	$C_2\wr C_2^2$ (as 16T128)	Trivial (GRH)
16.4.91376968498145132544.1	x¹⁶ - 8x¹⁴ + 38x¹² - 116x¹⁰ + 227x⁸ - 284x⁶ + 214x⁴ - 84x² + 9	\( 2^{28}\cdot 3^{10}\cdot 7^{8} \)	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.0.95224002328145166336.1	x¹⁶ - 4x¹⁵ + 6x¹³ + 35x¹² - 84x¹¹ + 101x¹⁰ - 202x⁹ + 456x⁸ - 722x⁷ + 761x⁶ - 564x⁵ + 311x⁴ - 126x³ + 39x² - 8x + 1	\( 2^{20}\cdot 3^{8}\cdot 7^{12} \)	$C_2\wr C_2^2$ (as 16T128)	$[2]$
16.4.109951162777600000000.1	x¹⁶ - 4x¹⁴ - 16x¹³ - 18x¹² + 48x¹¹ + 96x¹⁰ - 16x⁹ - 149x⁸ - 80x⁷ + 48x⁶ + 72x⁵ + 22x⁴ - 8x³ - 4x² - 1	\( 2^{48}\cdot 5^{8} \)	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.4.109951162777600000000.2	x¹⁶ - 4x¹⁴ + 6x¹² - 16x¹¹ - 8x¹⁰ + 24x⁹ + 15x⁸ - 80x⁷ + 208x⁶ - 256x⁵ + 194x⁴ + 8x³ - 76x² + 56x - 1	\( 2^{48}\cdot 5^{8} \)	$C_2\wr C_2^2$ (as 16T128)	Trivial (GRH)
16.0.119452832185734660096.2	x¹⁶ - 7x¹⁴ + 42x¹² - 136x¹⁰ + 262x⁸ - 243x⁶ + 174x⁴ + 90x² + 9	\( 2^{20}\cdot 3^{12}\cdot 11^{8} \)	$C_2\wr C_2^2$ (as 16T128)	$[2]$
16.0.149587343098087735296.7	x¹⁶ + 4x¹⁴ - 16x¹³ + 30x¹² - 48x¹¹ + 112x¹⁰ - 144x⁹ + 199x⁸ - 176x⁷ + 120x⁶ - 88x⁵ + 34x⁴ - 24x³ + 12x² + 3	\( 2^{48}\cdot 3^{12} \)	$C_2\wr C_2^2$ (as 16T128)	Trivial
16.4.822392716483306192896.1	x¹⁶ - 2x¹⁵ - 2x¹³ - 14x¹² + 6x¹¹ + 24x¹⁰ + 42x⁹ + 30x⁸ - 18x⁷ - 36x⁶ - 162x⁵ - 126x⁴ + 54x³ + 108x² + 162x + 81	\( 2^{28}\cdot 3^{12}\cdot 7^{8} \)	$C_2\wr C_2^2$ (as 16T128)	$[2]$
16.8.31130283153817600000000.1	x¹⁶ - 4x¹⁵ - 8x¹⁴ + 48x¹³ + 20x¹² - 228x¹¹ - 120x¹⁰ + 514x⁹ + 877x⁸ - 812x⁷ - 2696x⁶ + 1698x⁵ + 3167x⁴ - 2266x³ - 887x² + 738x - 41	\( 2^{24}\cdot 5^{8}\cdot 41^{6} \)	$C_2\wr C_2^2$ (as 16T128)	Trivial (GRH)
16.0.31130283153817600000000.2	x¹⁶ + 6x¹⁴ - 4x¹³ + 35x¹² + 8x¹¹ + 218x¹⁰ + 324x⁹ + 1031x⁸ + 1016x⁷ + 2078x⁶ + 1240x⁵ + 1681x⁴ - 152x³ + 1116x² - 1408x + 569	\( 2^{24}\cdot 5^{8}\cdot 41^{6} \)	$C_2\wr C_2^2$ (as 16T128)	$[2, 2]$
16.0.31130283153817600000000.3	x¹⁶ - 2x¹⁵ + 15x¹⁴ - 42x¹³ + 109x¹² - 262x¹¹ + 460x¹⁰ - 764x⁹ + 1239x⁸ - 1510x⁷ + 2094x⁶ - 2536x⁵ + 2266x⁴ - 2532x³ + 2010x² - 868x + 961	\( 2^{24}\cdot 5^{8}\cdot 41^{6} \)	$C_2\wr C_2^2$ (as 16T128)	$[4]$
16.8.189537365823025172265625.1	x¹⁶ - x¹⁵ - 8x¹⁴ - 17x¹³ - 30x¹² - 120x¹¹ - 227x¹⁰ - 72x⁹ - 46x⁸ - 167x⁷ - 342x⁶ - 300x⁵ + 205x⁴ + 148x³ - 78x² + 4x + 1	\( 5^{8}\cdot 13^{8}\cdot 29^{6} \)	$C_2\wr C_2^2$ (as 16T128)	Trivial (GRH)
16.0.74743809852316057600000000.1	x¹⁶ - 4x¹⁵ + 8x¹⁴ - 8x¹³ + 36x¹² - 124x¹¹ + 260x¹⁰ - 594x⁹ + 1345x⁸ - 1460x⁷ + 3872x⁶ - 6382x⁵ + 17487x⁴ - 6326x³ + 11745x² + 10382x + 37561	\( 2^{24}\cdot 5^{8}\cdot 7^{4}\cdot 41^{6} \)	$C_2\wr C_2^2$ (as 16T128)	$[2, 2, 18]$ (GRH)
16.16.74743809852316057600000000.1	x¹⁶ - 4x¹⁵ - 24x¹⁴ + 104x¹³ + 172x¹² - 876x¹¹ - 420x¹⁰ + 3082x⁹ - x⁸ - 4548x⁷ + 896x⁶ + 2246x⁵ - 217x⁴ - 362x³ + 3x² + 18x + 1	\( 2^{24}\cdot 5^{8}\cdot 7^{4}\cdot 41^{6} \)	$C_2\wr C_2^2$ (as 16T128)	Trivial (GRH)
16.0.338247889767883716141015625.2	x¹⁶ - 7x¹⁵ + 33x¹⁴ - 109x¹³ + 236x¹² - 29x¹¹ - 2203x¹⁰ + 9266x⁹ - 16826x⁸ - 12945x⁷ + 186735x⁶ - 673377x⁵ + 1554248x⁴ - 2544195x³ + 2937115x² - 2197228x + 824821	\( 5^{8}\cdot 13^{8}\cdot 101^{6} \)	$C_2\wr C_2^2$ (as 16T128)	$[44]$ (GRH)
16.16.620245622959489574938607616.1	x¹⁶ - 30x¹⁴ + 278x¹² - 1140x¹⁰ + 2280x⁸ - 2280x⁶ + 1112x⁴ - 240x² + 16	\( 2^{36}\cdot 3^{12}\cdot 19^{8} \)	$C_2\wr C_2^2$ (as 16T128)	Trivial (GRH)