### Supplement 1 to the paper "On the integrality of the Taylor coefficients of mirror maps" by Christian Krattenthaler and Tanguy Rivoal

The table below shows values of positive integers L <= 1000000 and prime numbers p <= L for which vp(HL) > 0.

The format of the table is:

{L, {{p, vp(HL)}, ...}

{7, {{3, 1}}}
{20, {{5, 1}}}
{22, {{3, 1}}}
{24, {{5, 1}}}
{42, {{7, 1}}}
{48, {{7, 1}}}
{77, {{11, 1}}}
{80, {{11, 1}}}
{84, {{11, 1}}}
{87, {{11, 1}}}
{110, {{11, 1}}}
{113, {{11, 1}}}
{117, {{11, 1}}}
{120, {{11, 1}}}
{156, {{13, 1}}}
{168, {{13, 1}}}
{272, {{17, 1}}}
{288, {{17, 1}}}
{295, {{7, 1}}}
{299, {{7, 1}}}
{337, {{7, 1}}}
{341, {{7, 1}}}
{342, {{19, 1}}}
{360, {{19, 1}}}
{386, {{29, 1}}}
{396, {{29, 1}}}
{440, {{29, 1}}}
{458, {{29, 1}}}
{506, {{23, 1}}}
{528, {{23, 1}}}
{622, {{61, 1}}}
{658, {{61, 1}}}
{692, {{137, 1}}}
{812, {{29, 1}}}
{814, {{137, 1}}}
{825, {{29, 1}}}
{827, {{29, 1}}}
{840, {{29, 1}}}
{848, {{11, 3}}}
{852, {{11, 1}}}
{856, {{11, 1}}}
{882, {{11, 1}}}
{888, {{11, 1}}}
{930, {{31, 1}}}
{958, {{11, 1}}}
{960, {{31, 1}}}
{962, {{11, 1}}}
{966, {{11, 1}}}
{1247, {{43, 1}}}
{1260, {{43, 1}}}
{1276, {{43, 1}}}
{1289, {{43, 1}}}
{1291, {{11, 1}}}
{1293, {{11, 1}}}
{1332, {{37, 1}}}
{1349, {{37, 1}}}
{1351, {{37, 1}}}
{1368, {{37, 1}}}
{1640, {{41, 1}}}
{1680, {{41, 1}}}
{1806, {{43, 1}}}
{1819, {{43, 1}}}
{1835, {{43, 1}}}
{1848, {{43, 1}}}
{2096, {{7, 1}}}
{2162, {{47, 1}}}
{2208, {{47, 1}}}
{2390, {{7, 1}}}
{2748, {{109, 1}}}
{2756, {{53, 1}}}
{2778, {{53, 1}}}
{2786, {{53, 1}}}
{2808, {{53, 1}}}
{2810, {{109, 1}}}
{3420, {{109, 2}}}
{3422, {{59, 1}}}
{3446, {{109, 1}}}
{3480, {{59, 1}}}
{3660, {{61, 1}}}
{3670, {{61, 1}}}
{3710, {{61, 1}}}
{3720, {{61, 1}}}
{4422, {{67, 1}}}
{4488, {{67, 1}}}
{4797, {{109, 1}}}
{4903, {{109, 1}}}
{4970, {{71, 1}}}
{5040, {{71, 1}}}
{5041, {{227, 1}}}
{5173, {{227, 1}}}
{5256, {{73, 1}}}
{5328, {{73, 1}}}
{6162, {{79, 1}}}
{6240, {{79, 1}}}
{6298, {{509, 1}}}
{6330, {{509, 1}}}
{6394, {{509, 1}}}
{6426, {{509, 1}}}
{6501, {{19, 1}}}
{6513, {{19, 1}}}
{6806, {{83, 1}}}
{6843, {{19, 1}}}
{6855, {{19, 1}}}
{6888, {{83, 1}}}
{7832, {{89, 1}}}
{7920, {{89, 1}}}
{8271, {{97, 1}}}
{8315, {{97, 1}}}
{8909, {{269, 1}}}
{9052, {{109, 1}}}
{9082, {{109, 1}}}
{9113, {{269, 1}}}
{9120, {{109, 1}}}
{9150, {{109, 1}}}
{9312, {{97, 1}}}
{9323, {{97, 2}}}
{9328, {{11, 2}}}
{9331, {{11, 1}}}
{9335, {{11, 1}}}
{9338, {{11, 3}}}
{9376, {{11, 1}}}
{9378, {{11, 1}}}
{9397, {{97, 1}}}
{9408, {{97, 1}}}
{9496, {{863, 1}}}
{10100, {{101, 1}}}
{10200, {{101, 1}}}
{10352, {{863, 1}}}
{10506, {{103, 1}}}
{10583, {{11, 3}}}
{10587, {{11, 1}}}
{10591, {{11, 2}}}
{10608, {{103, 1}}}
{11342, {{107, 1}}}
{11448, {{107, 1}}}
{11498, {{29, 1}}}
{11772, {{109, 1}}}
{11797, {{109, 1}}}
{11803, {{109, 1}}}
{11816, {{109, 1}}}
{11836, {{109, 1}}}
{11849, {{109, 1}}}
{11855, {{109, 1}}}
{11880, {{109, 1}}}
{12221, {{919, 1}}}
{12296, {{173, 1}}}
{12442, {{173, 1}}}
{12591, {{919, 1}}}
{12656, {{113, 1}}}
{12768, {{113, 1}}}
{14205, {{11, 1}}}
{14207, {{11, 1}}}
{14675, {{7, 1}}}
{15097, {{1049, 1}}}
{15323, {{1049, 1}}}
{16002, {{127, 1}}}
{16128, {{127, 1}}}
{16731, {{7, 1}}}
{16735, {{7, 1}}}
{17004, {{257, 1}}}
{17030, {{131, 1}}}
{17055, {{257, 1}}}
{17125, {{257, 1}}}
{17160, {{131, 1}}}
{17176, {{257, 1}}}
{18632, {{137, 1}}}
{18637, {{137, 1}}}
{18763, {{137, 1}}}
{18768, {{137, 1}}}
{19182, {{139, 1}}}
{19320, {{139, 1}}}
{22052, {{149, 1}}}
{22200, {{149, 1}}}
{22650, {{151, 1}}}
{22800, {{151, 1}}}
{23984, {{29, 1}}}
{23989, {{29, 1}}}
{24005, {{29, 1}}}
{24010, {{29, 1}}}
{24492, {{157, 1}}}
{24648, {{157, 1}}}
{26406, {{163, 1}}}
{26568, {{163, 1}}}
{27722, {{167, 1}}}
{27888, {{167, 1}}}
{28834, {{31, 1}}}
{28856, {{31, 1}}}
{29756, {{173, 1}}}
{29764, {{31, 1}}}
{29786, {{31, 1}}}
{29827, {{173, 1}}}
{29857, {{173, 1}}}
{29928, {{173, 1}}}
{30513, {{401, 1}}}
{30839, {{401, 1}}}
{31862, {{179, 1}}}
{32040, {{179, 1}}}
{32580, {{181, 1}}}
{32760, {{181, 1}}}
{32958, {{313, 1}}}
{33084, {{313, 1}}}
{36290, {{191, 1}}}
{36480, {{191, 1}}}
{37056, {{193, 1}}}
{37248, {{193, 1}}}
{38612, {{197, 1}}}
{38808, {{197, 1}}}
{39123, {{1019, 1}}}
{39339, {{1019, 1}}}
{39402, {{199, 1}}}
{39440, {{199, 1}}}
{39562, {{199, 1}}}
{39600, {{199, 1}}}
{39833, {{227, 1}}}
{39843, {{227, 1}}}
{42079, {{353, 1}}}
{42287, {{353, 1}}}
{44310, {{211, 1}}}
{44520, {{211, 1}}}
{49295, {{37, 1}}}
{49300, {{37, 1}}}
{49304, {{37, 1}}}
{49309, {{37, 1}}}
{49506, {{223, 1}}}
{49728, {{223, 1}}}
{50295, {{433, 1}}}
{50593, {{433, 1}}}
{50627, {{37, 1}}}
{50632, {{37, 1}}}
{50636, {{37, 1}}}
{50641, {{37, 1}}}
{51302, {{227, 1}}}
{51324, {{227, 1}}}
{51353, {{227, 1}}}
{51477, {{227, 1}}}
{51506, {{227, 1}}}
{51528, {{227, 1}}}
{52212, {{229, 1}}}
{52440, {{229, 1}}}
{53624, {{43, 1}}}
{53660, {{43, 1}}}
{54056, {{233, 1}}}
{54181, {{43, 1}}}
{54221, {{43, 1}}}
{54288, {{233, 1}}}
{54878, {{43, 1}}}
{54900, {{43, 1}}}
{55430, {{43, 1}}}
{55466, {{43, 1}}}
{56882, {{239, 1}}}
{57120, {{239, 1}}}
{57840, {{241, 1}}}
{58080, {{241, 1}}}
{62750, {{251, 1}}}
{63000, {{251, 1}}}
{65792, {{257, 1}}}
{65795, {{7129, 1}}}
{65858, {{257, 1}}}
{65982, {{257, 1}}}
{66048, {{257, 1}}}
{68906, {{263, 1}}}
{69168, {{263, 1}}}
{69655, {{7129, 1}}}
{72092, {{269, 1}}}
{72125, {{269, 1}}}
{72327, {{269, 1}}}
{72360, {{269, 1}}}
{73170, {{271, 1}}}
{73228, {{271, 1}}}
{73382, {{271, 1}}}
{73440, {{271, 1}}}
{76452, {{277, 1}}}
{76728, {{277, 1}}}
{78680, {{281, 1}}}
{78960, {{281, 1}}}
{79806, {{283, 1}}}
{80088, {{283, 1}}}
{85188, {{421, 1}}}
{85316, {{421, 1}}}
{85556, {{293, 1}}}
{85848, {{293, 1}}}
{87955, {{379, 1}}}
{88060, {{379, 1}}}
{88174, {{379, 1}}}
{88279, {{379, 1}}}
{91788, {{421, 1}}}
{91899, {{421, 1}}}
{92077, {{421, 1}}}
{92188, {{421, 1}}}
{93830, {{2917, 1}}}
{93942, {{307, 1}}}
{94248, {{307, 1}}}
{94830, {{137, 1}}}
{94837, {{137, 1}}}
{94854, {{137, 1}}}
{94890, {{137, 1}}}
{94907, {{137, 1}}}
{94914, {{137, 1}}}
{95774, {{2917, 1}}}
{96410, {{311, 1}}}
{96720, {{311, 1}}}
{97656, {{313, 1}}}
{97761, {{313, 1}}}
{97863, {{313, 1}}}
{97968, {{313, 1}}}
{98352, {{347, 1}}}
{98396, {{347, 1}}}
{100172, {{317, 1}}}
{100488, {{317, 1}}}
{101636, {{47, 1}}}
{101638, {{47, 1}}}
{102608, {{11, 1}}}
{102611, {{11, 1}}}
{102615, {{11, 1}}}
{102618, {{11, 1}}}
{102643, {{11, 1}}}
{102649, {{11, 1}}}
{102718, {{11, 2}}}
{102721, {{11, 2}}}
{102725, {{11, 1}}}
{102728, {{7, 1}, {11, 2}}}
{103798, {{47, 1}}}
{103800, {{47, 1}}}
{109230, {{331, 1}}}
{109560, {{331, 1}}}
{113232, {{337, 1}}}
{113568, {{337, 1}}}
{116413, {{11, 2}}}
{116416, {{11, 1}}}
{116420, {{11, 1}}}
{116423, {{11, 2}}}
{116501, {{11, 1}}}
{116504, {{11, 1}}}
{116508, {{11, 1}}}
{116511, {{11, 1}}}
{120062, {{347, 1}}}
{120125, {{347, 1}}}
{120345, {{347, 1}}}
{120408, {{347, 1}}}
{121452, {{349, 1}}}
{121800, {{349, 1}}}
{123433, {{3407, 1}}}
{123752, {{19, 2}}}
{123760, {{19, 1}}}
{124056, {{3407, 1}}}
{124256, {{353, 1}}}
{124375, {{353, 1}}}
{124489, {{353, 1}}}
{124608, {{353, 1}}}
{124654, {{3407, 1}}}
{125277, {{3407, 1}}}
{128522, {{359, 1}}}
{128880, {{359, 1}}}
{130254, {{19, 1}}}
{130635, {{2953, 1}}}
{132181, {{2953, 1}}}
{134322, {{367, 1}}}
{134688, {{367, 1}}}
{137269, {{8431, 1}}}
{138756, {{373, 1}}}
{139128, {{373, 1}}}
{140953, {{8431, 1}}}
{143262, {{379, 1}}}
{143358, {{397, 1}}}
{143408, {{379, 1}}}
{143494, {{379, 1}}}
{143640, {{379, 1}}}
{143672, {{397, 1}}}
{146094, {{53, 1}}}
{146306, {{383, 1}}}
{146688, {{383, 1}}}
{147682, {{53, 1}}}
{147686, {{53, 1}}}
{148850, {{53, 1}}}
{150575, {{941, 1}}}
{150932, {{389, 1}}}
{150970, {{941, 1}}}
{151090, {{941, 1}}}
{151320, {{389, 1}}}
{151485, {{941, 1}}}
{157212, {{397, 1}}}
{157247, {{397, 1}}}
{157573, {{397, 1}}}
{157608, {{397, 1}}}
{160400, {{401, 1}}}
{160476, {{401, 1}}}
{160724, {{401, 1}}}
{160800, {{401, 1}}}
{166872, {{409, 1}}}
{166992, {{409, 1}}}
{167160, {{409, 1}}}
{167280, {{409, 1}}}
{175142, {{419, 1}}}
{175560, {{419, 1}}}
{176820, {{421, 1}}}
{177022, {{421, 1}}}
{177038, {{421, 1}}}
{177240, {{421, 1}}}
{185330, {{431, 1}}}
{185760, {{431, 1}}}
{187056, {{433, 1}}}
{187172, {{433, 1}}}
{187372, {{433, 1}}}
{187488, {{433, 1}}}
{192282, {{439, 1}}}
{192495, {{439, 1}}}
{192507, {{439, 1}}}
{192720, {{439, 1}}}
{193865, {{4201, 1}}}
{195806, {{443, 1}}}
{196248, {{443, 1}}}
{196827, {{4201, 1}}}
{198725, {{1361, 2}}}
{200047, {{1361, 1}}}
{201152, {{449, 1}}}
{201600, {{449, 1}}}
{201918, {{59, 1}}}
{201936, {{59, 1}}}
{205340, {{59, 1}}}
{205358, {{59, 1}}}
{208392, {{457, 1}}}
{208848, {{457, 1}}}
{212060, {{461, 1}}}
{212520, {{461, 1}}}
{213906, {{463, 1}}}
{214368, {{463, 1}}}
{217622, {{467, 1}}}
{218088, {{467, 1}}}
{223268, {{61, 1}}}
{223312, {{61, 1}}}
{226928, {{61, 1}}}
{226972, {{61, 1}}}
{228962, {{479, 1}}}
{229440, {{479, 1}}}
{231756, {{1187, 1}}}
{232360, {{1187, 1}}}
{234512, {{1493, 1}}}
{235782, {{1493, 1}}}
{236682, {{487, 1}}}
{237168, {{487, 1}}}
{240590, {{491, 1}}}
{241080, {{491, 1}}}
{248502, {{499, 1}}}
{249000, {{499, 1}}}
{252506, {{503, 1}}}
{252682, {{971, 1}}}
{253008, {{503, 1}}}
{253208, {{971, 1}}}
{257943, {{947, 1}}}
{258171, {{947, 1}}}
{258572, {{509, 1}}}
{258584, {{509, 1}}}
{259068, {{509, 1}}}
{259080, {{509, 1}}}
{270920, {{521, 1}}}
{270947, {{521, 1}}}
{271226, {{1031, 1}}}
{271413, {{521, 1}}}
{271440, {{521, 1}}}
{272110, {{1031, 1}}}
{273006, {{523, 1}}}
{273528, {{523, 1}}}
{281022, {{1433, 1}}}
{281211, {{1433, 1}}}
{281688, {{761, 1}}}
{281784, {{761, 1}}}
{281957, {{1433, 1}}}
{282116, {{761, 1}}}
{282146, {{1433, 1}}}
{282212, {{761, 1}}}
{287232, {{641, 1}}}
{287744, {{641, 1}}}
{292140, {{541, 1}}}
{292680, {{541, 1}}}
{298391, {{1093, 1}}}
{298622, {{1093, 1}}}
{298662, {{547, 1}}}
{298842, {{1093, 1}}}
{299028, {{1093, 1}}}
{299208, {{547, 1}}}
{299248, {{1093, 2}}}
{299479, {{1093, 1}}}
{299560, {{109, 1}}}
{299612, {{109, 1}}}
{301816, {{1051, 1}}}
{302266, {{733, 1}}}
{302271, {{733, 1}}}
{302453, {{733, 1}}}
{302458, {{733, 1}}}
{302508, {{1051, 1}}}
{306303, {{109, 1}}}
{306385, {{109, 1}}}
{309276, {{10273, 1}}}
{309692, {{557, 1}}}
{310248, {{557, 1}}}
{315897, {{599, 1}}}
{315966, {{599, 1}}}
{315978, {{599, 1}}}
{316047, {{599, 1}}}
{316406, {{563, 1}}}
{316968, {{563, 1}}}
{317376, {{10273, 1}}}
{318577, {{577, 1}}}
{318698, {{577, 1}}}
{318886, {{577, 1}}}
{319007, {{577, 1}}}
{323192, {{569, 1}}}
{323760, {{569, 1}}}
{325175, {{3527, 1}}}
{325470, {{571, 1}}}
{326040, {{571, 1}}}
{326097, {{3527, 1}}}
{326397, {{3527, 1}}}
{327319, {{3527, 1}}}
{330231, {{9059, 1}}}
{331075, {{9059, 1}}}
{332352, {{577, 1}}}
{332376, {{577, 1}}}
{332904, {{577, 1}}}
{332928, {{577, 1}}}
{342441, {{1153, 1}}}
{342738, {{1153, 1}}}
{343296, {{1153, 1}}}
{343593, {{1153, 1}}}
{343982, {{587, 1}}}
{344568, {{587, 1}}}
{351056, {{593, 1}}}
{351648, {{593, 1}}}
{351788, {{821, 1}}}
{351796, {{821, 1}}}
{351800, {{821, 1}}}
{351808, {{821, 1}}}
{352891, {{71, 1}}}
{352902, {{71, 1}}}
{352908, {{71, 1}}}
{352919, {{71, 1}}}
{357861, {{71, 1}}}
{357872, {{71, 1}}}
{357878, {{71, 1}}}
{357889, {{71, 1}}}
{358202, {{599, 1}}}
{358273, {{599, 1}}}
{358729, {{599, 1}}}
{358800, {{599, 1}}}
{360600, {{601, 1}}}
{360794, {{601, 1}}}
{360832, {{601, 1}}}
{360968, {{601, 1}}}
{361006, {{601, 1}}}
{361200, {{601, 1}}}
{365951, {{2267, 1}}}
{366289, {{2267, 1}}}
{367842, {{607, 1}}}
{367844, {{2843, 1}}}
{368448, {{607, 1}}}
{368492, {{2843, 1}}}
{372780, {{109, 1}}}
{372805, {{109, 1}}}
{372811, {{109, 1}}}
{372824, {{109, 1}}}
{372844, {{109, 1}}}
{372857, {{109, 1}}}
{372863, {{109, 1}}}
{372888, {{109, 1}}}
{375156, {{613, 1}}}
{375768, {{613, 1}}}
{380072, {{617, 1}}}
{380171, {{617, 1}}}
{380589, {{617, 1}}}
{380688, {{617, 1}}}
{382542, {{619, 1}}}
{383160, {{619, 1}}}
{397530, {{631, 1}}}
{398160, {{631, 1}}}
{407016, {{677, 1}}}
{407414, {{677, 1}}}
{410240, {{641, 1}}}
{410432, {{641, 1}}}
{410473, {{641, 1}}}
{410647, {{641, 1}}}
{410688, {{641, 1}}}
{410880, {{641, 1}}}
{412806, {{643, 1}}}
{413024, {{643, 1}}}
{413230, {{643, 1}}}
{413448, {{643, 1}}}
{417962, {{647, 1}}}
{418057, {{647, 1}}}
{418513, {{647, 1}}}
{418608, {{647, 1}}}
{425756, {{653, 1}}}
{426408, {{653, 1}}}
{433622, {{659, 1}}}
{433725, {{659, 1}}}
{434177, {{659, 1}}}
{434280, {{659, 1}}}
{435069, {{1009, 1}}}
{435697, {{1009, 1}}}
{436260, {{661, 1}}}
{436920, {{661, 1}}}
{437089, {{1433, 1}}}
{438473, {{1433, 1}}}
{438483, {{1373, 1}}}
{438863, {{1373, 1}}}
{452256, {{673, 1}}}
{452928, {{673, 1}}}
{457652, {{677, 1}}}
{457727, {{677, 1}}}
{458253, {{677, 1}}}
{458328, {{677, 1}}}
{465806, {{683, 1}}}
{466488, {{683, 1}}}
{467099, {{2731, 1}}}
{467878, {{2731, 1}}}
{467931, {{2689, 1}}}
{468854, {{2731, 1}}}
{469633, {{2731, 1}}}
{470529, {{2689, 1}}}
{471573, {{2927, 1}}}
{472459, {{2927, 1}}}
{472961, {{2927, 1}}}
{473847, {{2927, 1}}}
{476790, {{691, 1}}}
{477480, {{691, 1}}}
{488406, {{4139, 1}}}
{490700, {{701, 1}}}
{491254, {{1637, 1}}}
{491379, {{1289, 1}}}
{491400, {{701, 1}}}
{491831, {{1637, 1}}}
{492005, {{1637, 1}}}
{492127, {{1289, 1}}}
{492481, {{9103, 1}}}
{492536, {{4139, 1}}}
{492582, {{1637, 1}}}
{499745, {{9103, 1}}}
{501972, {{709, 1}}}
{502680, {{709, 1}}}
{516242, {{719, 1}}}
{516960, {{719, 1}}}
{517816, {{971, 1}}}
{518240, {{971, 1}}}
{520009, {{2557, 1}}}
{520689, {{2557, 1}}}
{522919, {{109, 1}}}
{522935, {{109, 1}}}
{523599, {{1543, 1}}}
{524097, {{1543, 1}}}
{527802, {{727, 1}}}
{528528, {{727, 1}}}
{528660, {{3671, 1}}}
{532258, {{3671, 1}}}
{532576, {{1439, 1}}}
{533722, {{1439, 1}}}
{534531, {{17783, 1}}}
{536556, {{733, 1}}}
{536876, {{733, 1}}}
{536968, {{733, 1}}}
{537288, {{733, 1}}}
{545314, {{2749, 1}}}
{545382, {{739, 1}}}
{546038, {{2749, 1}}}
{546120, {{739, 1}}}
{550231, {{17783, 1}}}
{551306, {{743, 1}}}
{552048, {{743, 1}}}
{560973, {{761, 1}}}
{561501, {{761, 1}}}
{563250, {{751, 1}}}
{564000, {{751, 1}}}
{564924, {{83, 1}}}
{564954, {{83, 1}}}
{571730, {{83, 1}}}
{571760, {{83, 1}}}
{572292, {{757, 1}}}
{573048, {{757, 1}}}
{578360, {{761, 1}}}
{578368, {{761, 1}}}
{578383, {{761, 1}}}
{578730, {{761, 1}}}
{578750, {{761, 1}}}
{579097, {{761, 1}}}
{579112, {{761, 1}}}
{579120, {{761, 1}}}
{590592, {{769, 1}}}
{591360, {{769, 1}}}
{594040, {{4273, 1}}}
{594774, {{947, 1}}}
{594790, {{947, 1}}}
{595588, {{947, 1}}}
{595604, {{947, 1}}}
{596756, {{773, 1}}}
{596895, {{773, 1}}}
{597389, {{773, 1}}}
{597528, {{773, 1}}}
{598126, {{4273, 1}}}
{602980, {{809, 1}}}
{603238, {{809, 1}}}
{618582, {{787, 1}}}
{619368, {{787, 1}}}
{622254, {{41233, 1}}}
{626097, {{5531, 1}}}
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