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{'Lhash': '1542172351877527543040705654908,1620396047735205305480709742703,1677147726419609307626980508034', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': -3, 'a6': 0, 'a7': -8, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 209676.67819583448, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -3, 3, -1]], [5, [1, 3, 3, 1]], [31, [1, 3, 3, 1]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '7440.1', 'coefficient_field': '1.1.1.1', 'conductor': 411830784000, 'conductor_radical': 930, 'degree': 6, 'euler_factors': [[1], [1, -3, 3, -1], [1, 3, 3, 1], [1, 8, 37, 118, 259, 392, 343], [1, 2, 13, 20, 143, 242, 1331], [1, -4, 39, -98, 507, -676, 2197], [1, -4, 47, -132, 799, -1156, 4913], [1, -4, 25, -56, 475, -1444, 6859], [1, 6, 57, 272, 1311, 3174, 12167], [1, 2, 21, 230, 609, 1682, 24389], [1, 3, 3, 1], [1, -10, 139, -758, 5143, -13690, 50653], [1, 8, 123, 608, 5043, 13448, 68921], [1, 10, 141, 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'5.44308686489062930668853587345224', '5.44685960345031303759820765073329', '5.65831262539133229581415519384286', '6.07102305949354961583652814086610', '6.26974359568956614732909468392280', '6.34604810361562021801944905498232', '6.80677301236693434501980084215737', '6.91142475646651734587028612605236', '7.15418654600094475815254049823526', '7.40778753109173572012781677151046', '7.59426270534025361754137830631921', '7.67256400962616786916977662775459'], 'prelabel': '6-7440e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.707703880133994, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1e3-0', 'trace_hash': 1747348851030763457, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21655947750892312251002142585', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.27826709303294391363430137420', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.32303627365273485511921691362', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 209676.67819583448, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 411830784000, 'conductor_radical': 930, 'degree': 6, 'dirichlet_coefficients': [1, 0, 3, 0, -3, 0, -8, 0, 6, 0, -2, 0, 4, 0, -9, 0, 4, 0, 4, 0, -24, 0, -6, 0, 6, 0, 10, 0, -2, 0, -3, 0, -6, 0, 24, 0, 10, 0, 12, 0, -8, 0, -10, 0, -18, 0, 10, 0, 27, 0, 12, 0, 0, 0, 6, 0, 12, 0, 8, 0, -6, 0, -48, 0, -12, 0, -18, 0, -18, 0, -10, 0, 18, 0, 18, 0, 16, 0, -20, 0, 15, 0, -22, 0, -12, 0, -6, 0, 8, 0, -32, 0, -9, 0, -12, 0, 8, 0, -12, 0], 'euler11': [1, 2, 13, 20, 143, 242, 1331], 'euler13': [1, -4, 39, -98, 507, -676, 2197], 'euler17': [1, -4, 47, -132, 799, -1156, 4913], 'euler19': [1, -4, 25, -56, 475, -1444, 6859], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, 6, 57, 272, 1311, 3174, 12167], 'euler29': [1, 2, 21, 230, 609, 1682, 24389], 'euler3': [1, -3, 3, -1, 0, 0, 0], 'euler31': [1, 3, 3, 1, 0, 0, 0], 'euler37': [1, -10, 139, -758, 5143, -13690, 50653], 'euler41': [1, 8, 123, 608, 5043, 13448, 68921], 'euler43': [1, 10, 141, 836, 6063, 18490, 79507], 'euler47': [1, -10, 89, -432, 4183, -22090, 103823], 'euler5': [1, 3, 3, 1, 0, 0, 0], 'euler53': [1, 0, 135, -36, 7155, 0, 148877], 'euler59': [1, -8, 187, -938, 11033, -27848, 205379], 'euler61': [1, 6, 195, 740, 11895, 22326, 226981], 'euler67': [1, 18, 273, 2330, 18291, 80802, 300763], 'euler7': [1, 8, 37, 118, 259, 392, 343], 'euler71': [1, 10, 147, 1162, 10437, 50410, 357911], 'euler73': [1, -18, 279, -2522, 20367, -95922, 389017], 'euler79': [1, 20, 333, 3124, 26307, 124820, 493039], 'euler83': [1, 22, 325, 3160, 26975, 151558, 571787], 'euler89': [1, -8, 5, -30, 445, -63368, 704969], 'euler97': [1, -8, 123, -64, 11931, -75272, 912673], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, -3, 3, -1, 0, 0, 0], [1, 3, 3, 1, 0, 0, 0], [1, 8, 37, 118, 259, 392, 343], [1, 2, 13, 20, 143, 242, 1331], [1, -4, 39, -98, 507, -676, 2197], [1, -4, 47, -132, 799, -1156, 4913], [1, -4, 25, -56, 475, -1444, 6859], [1, 6, 57, 272, 1311, 3174, 12167], [1, 2, 21, 230, 609, 1682, 24389], [1, 3, 3, 1, 0, 0, 0], [1, -10, 139, -758, 5143, -13690, 50653], [1, 8, 123, 608, 5043, 13448, 68921], [1, 10, 141, 836, 6063, 18490, 79507], [1, -10, 89, -432, 4183, -22090, 103823], [1, 0, 135, -36, 7155, 0, 148877], [1, -8, 187, -938, 11033, -27848, 205379], [1, 6, 195, 740, 11895, 22326, 226981], [1, 18, 273, 2330, 18291, 80802, 300763], [1, 10, 147, 1162, 10437, 50410, 357911], [1, -18, 279, -2522, 20367, -95922, 389017], [1, 20, 333, 3124, 26307, 124820, 493039], [1, 22, 325, 3160, 26975, 151558, 571787], [1, -8, 5, -30, 445, -63368, 704969], [1, -8, 123, -64, 11931, -75272, 912673]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7440/2/a/bs'], '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': '6-7440e3-1.1-c1e3-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 3, 'prelabel': '6-7440e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.707703880133994, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 1747348851030763457, 'z1': {'__RealLiteral__': 0, 'data': '1.21655947750892312251002142585', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1542172351877527543040705654908,1620396047735205305480709742703,1677147726419609307626980508034', 'Lhash_array': ['1542172351877527543040705654908', '1620396047735205305480709742703', '1677147726419609307626980508034'], 'factors': ['2-7440-1.1-c1-0-82', '2-7440-1.1-c1-0-91', '2-7440-1.1-c1-0-95'], 'label': '6-7440e3-1.1-c1e3-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7440/2/a/bs'}