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  • lfunc_lfunctions • Show schema
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'13.88645216570967729365082955251098', '14.03025659970480124915438553698574', '14.03548670747572568608899896912458', '14.27618193468874764266538236533511', '14.30789900657442908276407978795590', '14.48274740407572000783809724053777', '14.76410687475959123615892895819769', '14.92765749725931058585307823019136', '14.98843911517951175334623654254228', '15.13384740648280833474300574341188', '15.65056028042944147605242121622897', '15.86882622858447857514556964062459'], 'prelabel': '12-57e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.6746460490666928, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e6-0', 'trace_hash': 2012265311906255840, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.12470280408781661591321108240', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.42377951463254828862478205074', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.22988379104188754171975527228', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.008890205012281008, 'bad_primes': [3, 19], 'central_character': '1.1', 'conductor': 34296447249, 'conductor_radical': 57, 'degree': 12, 'dirichlet_coefficients': [1, 3, 0, 3, -6, 0, 3, -1, 0, -18, 3, 0, -6, 9, 0, -12, -12, 0, 18, -18, 0, 9, -9, 0, 18, -18, 1, 9, 12, 0, -24, -24, 0, -36, -18, 0, 12, 54, 0, 6, 6, 0, 18, 9, 0, -27, -33, 0, 21, 54, 0, -18, -24, 3, -18, -3, 0, 36, 0, 0, -21, -72, 0, -19, 36, 0, 30, -36, 0, -54, 18, 0, -27, 36, 0, 54, 9, 0, 12, 72, 0, 18, 15, 0, 72, 54, 0, -3, 45, 0, -18, -27, 0, -99, -108, 0, 21, 63, 0, 54], 'euler11': [1, -3, -6, 13, -27, 192, -61, 2112, -3267, 17303, -87846, -483153, 1771561], 'euler13': [1, 6, 30, 86, 288, 180, 231, 2340, 48672, 188942, 856830, 2227758, 4826809], 'euler17': [1, 12, 114, 809, 4965, 25191, 111881, 428247, 1434885, 3974617, 9521394, 17038284, 24137569], 'euler19': [1, -18, 162, -883, 3078, -6498, 6859, 0, 0, 0, 0, 0, 0], 'euler2': [1, -3, 6, -8, 15, -27, 47, -54, 60, -64, 96, -96, 64], 'euler23': [1, 9, 18, -130, -603, 4725, 49121, 108675, -318987, -1581710, 5037138, 57927087, 148035889], 'euler29': [1, -12, 60, -26, -1200, 9792, -51073, 283968, -1009200, -634114, 42436860, -246133788, 594823321], 'euler3': [1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0], 'euler31': [1, 24, 294, 2814, 23334, 160962, 949331, 4989822, 22423974, 83831874, 271515174, 687099624, 887503681], 'euler37': [1, -12, 240, -2010, 22668, -141888, 1124219, -5249856, 31032492, -101812530, 449798640, -832127484, 2565726409], 'euler41': [1, -6, 81, -351, 4257, -12003, 138106, -492123, 7156017, -24191271, 228886641, -695137206, 4750104241], 'euler43': [1, -18, 144, -520, 2610, -49554, 474393, -2130822, 4825890, -41343640, 492307344, -2646151974, 6321363049], 'euler47': [1, 33, 477, 3357, 648, -230538, -2370995, -10835286, 1431432, 348533811, 2327607837, 7568385231, 10779215329], 'euler5': [1, 6, 18, 45, 81, 87, 109, 435, 2025, 5625, 11250, 18750, 15625], 'euler53': [1, 24, 375, 4609, 47013, 413955, 3190646, 21939615, 132059517, 686174093, 2958930375, 10036691832, 22164361129], 'euler59': [1, 0, 54, 661, 5391, 27351, 485585, 1613709, 18766071, 135755519, 654337494, 0, 42180533641], 'euler61': [1, 21, 204, 872, -5166, -119673, -1122129, -7300053, -19222686, 197927432, 2824551564, 17736522321, 51520374361], 'euler67': [1, -30, 372, -1966, -7344, 261360, -2850267, 17511120, -32967216, -591300058, 7496217012, -40503753210, 90458382169], 'euler7': [1, -3, -12, 19, 171, -126, -1161, -882, 8379, 6517, -28812, -50421, 117649], 'euler71': [1, -18, 144, -180, -4734, 88470, -842507, 6281370, -23864094, -64423980, 3659282064, -32476128318, 128100283921], 'euler73': [1, 27, 324, 2356, 4887, -141291, -1960287, -10314243, 26042823, 916524052, 9201030084, 55972933011, 151334226289], 'euler79': [1, -12, 168, -1772, 24948, -218700, 2149713, -17277300, 155700468, -873665108, 6543613608, -36924676788, 243087455521], 'euler83': [1, -15, -60, 603, 20985, -88800, -1199405, -7370400, 144565665, 344787561, -2847499260, -59085609645, 326940373369], 'euler89': [1, -45, 900, -9000, 10575, 1004445, -14638319, 89395605, 83764575, -6344721000, 56468016900, -251282675205, 496981290961], 'euler97': [1, -21, 210, -814, -6003, 250281, -3257067, 24277257, -56482227, -742915822, 18591149010, -180334145397, 832972004929], 'euler_factors': [[1, -3, 6, -8, 15, -27, 47, -54, 60, -64, 96, -96, 64], [1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 6, 18, 45, 81, 87, 109, 435, 2025, 5625, 11250, 18750, 15625], [1, -3, -12, 19, 171, -126, -1161, -882, 8379, 6517, -28812, -50421, 117649], [1, -3, -6, 13, -27, 192, -61, 2112, -3267, 17303, -87846, -483153, 1771561], [1, 6, 30, 86, 288, 180, 231, 2340, 48672, 188942, 856830, 2227758, 4826809], [1, 12, 114, 809, 4965, 25191, 111881, 428247, 1434885, 3974617, 9521394, 17038284, 24137569], [1, -18, 162, -883, 3078, -6498, 6859, 0, 0, 0, 0, 0, 0], [1, 9, 18, -130, -603, 4725, 49121, 108675, -318987, -1581710, 5037138, 57927087, 148035889], [1, -12, 60, -26, -1200, 9792, -51073, 283968, -1009200, -634114, 42436860, -246133788, 594823321], [1, 24, 294, 2814, 23334, 160962, 949331, 4989822, 22423974, 83831874, 271515174, 687099624, 887503681], [1, -12, 240, -2010, 22668, -141888, 1124219, -5249856, 31032492, -101812530, 449798640, -832127484, 2565726409], [1, -6, 81, -351, 4257, -12003, 138106, -492123, 7156017, -24191271, 228886641, -695137206, 4750104241], [1, -18, 144, -520, 2610, -49554, 474393, -2130822, 4825890, -41343640, 492307344, -2646151974, 6321363049], [1, 33, 477, 3357, 648, -230538, -2370995, -10835286, 1431432, 348533811, 2327607837, 7568385231, 10779215329], [1, 24, 375, 4609, 47013, 413955, 3190646, 21939615, 132059517, 686174093, 2958930375, 10036691832, 22164361129], [1, 0, 54, 661, 5391, 27351, 485585, 1613709, 18766071, 135755519, 654337494, 0, 42180533641], [1, 21, 204, 872, -5166, -119673, -1122129, -7300053, -19222686, 197927432, 2824551564, 17736522321, 51520374361], [1, -30, 372, -1966, -7344, 261360, -2850267, 17511120, -32967216, -591300058, 7496217012, -40503753210, 90458382169], [1, -18, 144, -180, -4734, 88470, -842507, 6281370, -23864094, -64423980, 3659282064, -32476128318, 128100283921], [1, 27, 324, 2356, 4887, -141291, -1960287, -10314243, 26042823, 916524052, 9201030084, 55972933011, 151334226289], [1, -12, 168, -1772, 24948, -218700, 2149713, -17277300, 155700468, -873665108, 6543613608, -36924676788, 243087455521], [1, -15, -60, 603, 20985, -88800, -1199405, -7370400, 144565665, 344787561, -2847499260, -59085609645, 326940373369], [1, -45, 900, -9000, 10575, 1004445, -14638319, 89395605, 83764575, -6344721000, 56468016900, -251282675205, 496981290961], [1, -21, 210, -814, -6003, 250281, -3257067, 24277257, -56482227, -742915822, 18591149010, -180334145397, 832972004929]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/57/2/i/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '12-57e6-1.1-c1e6-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0, 0, 0], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '12-57e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.6746460490666928, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 2012265311906255840, 'z1': {'__RealLiteral__': 0, 'data': '2.12470280408781661591321108240', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2693380784908522835187681007436,3072505556544836365588734426550,4094364126381677811926965594315,4298097770817239982578176178515,4607725769537792654218392985720,5508090243571326518855334839964', 'Lhash_array': ['2693380784908522835187681007436', '3072505556544836365588734426550', '4094364126381677811926965594315', '4298097770817239982578176178515', '4607725769537792654218392985720', '5508090243571326518855334839964'], 'factors': ['2-57-19.9-c1-0-0', '2-57-19.6-c1-0-1', '2-57-19.16-c1-0-1', '2-57-19.5-c1-0-2', '2-57-19.4-c1-0-2', '2-57-19.17-c1-0-2'], 'label': '12-57e6-1.1-c1e6-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/57/2/i/a'}