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lfunc_lfunctions • Show schema
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{'Lhash': '2081852397938563224775904737475', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5331277188085841, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]]], 'bad_primes': [2, 3], 'central_character': '192.1', 'coefficient_field': '1.1.1.1', 'conductor': 192, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -2, 5], [1, 0, 7], [1, -4, 11], [1, -2, 13], [1, -2, 17], [1, 4, 19], [1, -8, 23], [1, 6, 29], [1, 8, 31], [1, 6, 37], [1, 6, 41], [1, -4, 43], [1, 0, 47], [1, -2, 53], [1, -4, 59], [1, -2, 61], [1, 4, 67], [1, 8, 71], [1, -10, 73], [1, -8, 79], [1, 4, 83], [1, 6, 89], [1, -2, 97], [1, -18, 101], [1, 16, 103], [1, 12, 107], [1, -2, 109], [1, -18, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, -2, 5], 1]], [[[1, 0, 7], 1]], [[[1, -4, 11], 1]], [[[1, -2, 13], 1]], [[[1, -2, 17], 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1.432346124715246, -0.21389410116597063, -2.0358356627367784, -3.665926167616059, -4.776470486092789, -5.158318489351172, -4.769713066375536, -3.742563744811441], 'positive_zeros': ['1.64229196717434907696557687174643', '3.71523857372513194753595622108180', '5.24179959934618595033608799542342', '6.21040581024747445781537308376326', '7.13146007277855219299925953914547', '8.777512613188475551383845278967670', '9.549120050570062839357860330869259', '10.68009321996461187722201460512165', '11.45788576598466513578332775969416', '12.60302456212821382428532603865363'], 'prelabel': '2-192-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.2381953475960827, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1223676697033421233, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.64229196717434907696557687175', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.71523857372513194753595622108', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.24179959934618595033608799542', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5331277188085841, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 192, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 2, 0, 0, 0, 1, 0, 4, 0, 2, 0, -2, 0, 2, 0, -4, 0, 0, 0, 8, 0, -1, 0, -1, 0, -6, 0, -8, 0, -4, 0, 0, 0, -6, 0, -2, 0, -6, 0, 4, 0, 2, 0, 0, 0, -7, 0, -2, 0, 2, 0, 8, 0, 4, 0, 4, 0, 2, 0, 0, 0, 4, 0, -4, 0, -8, 0, -8, 0, 10, 0, 1, 0, 0, 0, 8, 0, 1, 0, -4, 0, 4, 0, 6, 0, -6, 0, 0, 0, 8, 0, -8, 0, 2, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, -2, 13], 'euler17': [1, -2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, 6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 8, 31], 'euler37': [1, 6, 37], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, 0, 47], 'euler5': [1, -2, 5], 'euler53': [1, -2, 53], 'euler59': [1, -4, 59], 'euler61': [1, -2, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 7], 'euler71': [1, 8, 71], 'euler73': [1, -10, 73], 'euler79': [1, -8, 79], 'euler83': [1, 4, 83], 'euler89': [1, 6, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -2, 5], [1, 0, 7], [1, -4, 11], [1, -2, 13], [1, -2, 17], [1, 4, 19], [1, -8, 23], [1, 6, 29], [1, 8, 31], [1, 6, 37], [1, 6, 41], [1, -4, 43], [1, 0, 47], [1, -2, 53], [1, -4, 59], [1, -2, 61], [1, 4, 67], [1, 8, 71], [1, -10, 73], [1, -8, 79], [1, 4, 83], [1, 6, 89], [1, -2, 97]], 'index': 0, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/192/b', 'ModularForm/GL2/Q/holomorphic/192/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/192/2/a/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-192-1.1-c1-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-192-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.2381953475960827, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1223676697033421233, 'z1': {'__RealLiteral__': 0, 'data': '1.64229196717434907696557687175', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10022673
{'Lhash': '2081852397938563224775904737475', 'Lhash_array': ['2081852397938563224775904737475'], 'label': '2-192-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/2/a/b'}
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id: 24547941
{'Lhash': '2081852397938563224775904737475', 'Lhash_array': ['2081852397938563224775904737475'], 'label': '2-192-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/2/a/b/1/1'}
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id: 21990
{'Lhash': '1223676697033421233', 'Lhash_array': ['1223676697033421233'], 'label': '2-192-1.1-c1-0-0', 'type': 'ECQ', 'url': 'EllipticCurve/Q/192/b'}