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lfunc_lfunctions • Show schema
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{'Lhash': '1565190358319582476048926875645', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 49.826650861278985, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, -1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '6240.1', 'coefficient_field': '1.1.1.1', 'conductor': 6240, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -1], [1, 1, 7], [1, 1, 11], [1, 1], [1, 5, 17], [1, -2, 19], [1, -7, 23], [1, 0, 29], [1, -4, 31], [1, 7, 37], [1, 11, 41], [1, -6, 43], [1, 0, 47], [1, -11, 53], [1, -4, 59], [1, 7, 61], [1, -8, 67], [1, 9, 71], [1, -2, 73], [1, -3, 79], [1, 0, 83], [1, -3, 89], [1, -7, 97], [1, 12, 101], [1, 4, 103], [1, 13, 107], [1, 4, 109], [1, 14, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, -1], 1]], [[[1, 1, 7], 1]], [[[1, 1, 11], 1]], [[[1, 1], 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0.4465096273845879, -0.00015606444231587805, -0.4195990266191961, -0.7890702679172397, -1.0882948268783321, -1.3006041162479907, -1.4138796084290464, -1.4212534269895072, -1.3215243515754775], 'positive_zeros': ['1.23471748290718565818333854990345', '2.32797933687062497279664947021541', '3.12826551564954722904304742529129', '4.13233725858994189975801585819084', '5.05706220517884585286969524262763', '5.37480164731559533044183587889991', '6.48002794249954885136321718434919', '6.76932515933827549795396792826057', '7.52497049284418959018797916221192'], 'prelabel': '2-6240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.058799534005693, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 195248396280836937, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23471748290718565818333854990', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.32797933687062497279664947022', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.12826551564954722904304742529', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 49.826650861278985, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 6240, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, 0, -1, 0, -5, 0, 2, 0, 1, 0, 7, 0, 1, 0, -1, 0, 0, 0, 4, 0, 1, 0, -1, 0, -7, 0, 1, 0, -11, 0, 6, 0, 1, 0, 0, 0, -6, 0, 5, 0, 11, 0, -1, 0, -2, 0, 4, 0, -7, 0, -1, 0, -1, 0, 8, 0, -7, 0, -9, 0, 2, 0, -1, 0, 1, 0, 3, 0, 1, 0, 0, 0, -5, 0, 0, 0, 3, 0, 1, 0, -4, 0, 2, 0, 7, 0, -1, 0], 'euler11': [1, 1, 11], 'euler13': [1, 1, 0], 'euler17': [1, 5, 17], 'euler19': [1, -2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -7, 23], 'euler29': [1, 0, 29], 'euler3': [1, 1, 0], 'euler31': [1, -4, 31], 'euler37': [1, 7, 37], 'euler41': [1, 11, 41], 'euler43': [1, -6, 43], 'euler47': [1, 0, 47], 'euler5': [1, -1, 0], 'euler53': [1, -11, 53], 'euler59': [1, -4, 59], 'euler61': [1, 7, 61], 'euler67': [1, -8, 67], 'euler7': [1, 1, 7], 'euler71': [1, 9, 71], 'euler73': [1, -2, 73], 'euler79': [1, -3, 79], 'euler83': [1, 0, 83], 'euler89': [1, -3, 89], 'euler97': [1, -7, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -1, 0], [1, 1, 7], [1, 1, 11], [1, 1, 0], [1, 5, 17], [1, -2, 19], [1, -7, 23], [1, 0, 29], [1, -4, 31], [1, 7, 37], [1, 11, 41], [1, -6, 43], [1, 0, 47], [1, -11, 53], [1, -4, 59], [1, 7, 61], [1, -8, 67], [1, 9, 71], [1, -2, 73], [1, -3, 79], [1, 0, 83], [1, -3, 89], [1, -7, 97]], 'index': 65, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6240/i', 'ModularForm/GL2/Q/holomorphic/6240/2/a/i/1/1', 'ModularForm/GL2/Q/holomorphic/6240/2/a/i'], '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': '2-6240-1.1-c1-0-65', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-6240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.058799534005693, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 195248396280836937, 'z1': {'__RealLiteral__': 0, 'data': '1.23471748290718565818333854990', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21572015
{'Lhash': '1565190358319582476048926875645', 'Lhash_array': ['1565190358319582476048926875645'], 'label': '2-6240-1.1-c1-0-65', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6240/2/a/i'}
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id: 24574084
{'Lhash': '1565190358319582476048926875645', 'Lhash_array': ['1565190358319582476048926875645'], 'label': '2-6240-1.1-c1-0-65', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6240/2/a/i/1/1'}
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id: 37897
{'Lhash': '195248396280836937', 'Lhash_array': ['195248396280836937'], 'label': '2-6240-1.1-c1-0-65', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6240/i'}