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lfunc_lfunctions • Show schema
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{'Lhash': '1638742919452871267742973288549', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 53.659470158300444, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, -1]], [7, [1, 1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '6720.1', 'coefficient_field': '1.1.1.1', 'conductor': 6720, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -1], [1, 1], [1, -4, 11], [1, 2, 13], [1, 2, 17], [1, 0, 19], [1, 4, 23], [1, 2, 29], [1, -8, 31], [1, 10, 37], [1, -2, 41], [1, 4, 43], [1, -4, 47], [1, 10, 53], [1, 4, 59], [1, -2, 61], [1, 4, 67], [1, 0, 71], [1, 6, 73], [1, -8, 79], [1, -4, 83], [1, 6, 89], [1, -10, 97], [1, 18, 101], [1, 16, 103], [1, -4, 107], [1, -2, 109], [1, -6, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, -1], 1]], [[[1, 1], 1]], [[[1, -4, 11], 1]], [[[1, 2, 13], 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0.08870577384683688, -0.3039139328285363, -0.6478543232497488, -0.9259523157477085, -1.1252946029481923, -1.237970376257691, -1.2615389181984087, -1.1991826409335093, -1.0595337978098656], 'positive_zeros': ['1.29274022286411566435418517820576', '2.16052316781545979481240732017193', '3.22161536700473540275064515910922', '4.10303769011681448379978360486611', '4.76903688268145631571629079075587', '5.59839104524026054435120119507509', '6.35740963042324510115864982203606', '6.69037211824185238954732667899755', '7.48430302303971616673916615948432'], 'prelabel': '2-6720-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.325262463441187, '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': 1860672303978511092, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29274022286411566435418517821', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.16052316781545979481240732017', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.22161536700473540275064515911', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 53.659470158300444, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 6720, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 4, 0, -2, 0, -1, 0, -2, 0, 0, 0, 1, 0, -4, 0, 1, 0, -1, 0, -2, 0, 8, 0, -4, 0, -1, 0, -10, 0, 2, 0, 2, 0, -4, 0, 1, 0, 4, 0, 1, 0, 2, 0, -10, 0, 4, 0, 0, 0, -4, 0, 2, 0, -1, 0, -2, 0, -4, 0, 4, 0, 0, 0, -6, 0, -1, 0, -4, 0, 8, 0, 1, 0, 4, 0, -2, 0, 2, 0, -6, 0, 2, 0, -8, 0, 0, 0, 10, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, 2, 13], 'euler17': [1, 2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, 2, 29], 'euler3': [1, 1, 0], 'euler31': [1, -8, 31], 'euler37': [1, 10, 37], 'euler41': [1, -2, 41], 'euler43': [1, 4, 43], 'euler47': [1, -4, 47], 'euler5': [1, -1, 0], 'euler53': [1, 10, 53], 'euler59': [1, 4, 59], 'euler61': [1, -2, 61], 'euler67': [1, 4, 67], 'euler7': [1, 1, 0], 'euler71': [1, 0, 71], 'euler73': [1, 6, 73], 'euler79': [1, -8, 79], 'euler83': [1, -4, 83], 'euler89': [1, 6, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -1, 0], [1, 1, 0], [1, -4, 11], [1, 2, 13], [1, 2, 17], [1, 0, 19], [1, 4, 23], [1, 2, 29], [1, -8, 31], [1, 10, 37], [1, -2, 41], [1, 4, 43], [1, -4, 47], [1, 10, 53], [1, 4, 59], [1, -2, 61], [1, 4, 67], [1, 0, 71], [1, 6, 73], [1, -8, 79], [1, -4, 83], [1, 6, 89], [1, -10, 97]], 'index': 69, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6720/v', 'ModularForm/GL2/Q/holomorphic/6720/2/a/v/1/1', 'ModularForm/GL2/Q/holomorphic/6720/2/a/v'], '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': '2-6720-1.1-c1-0-69', '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': '2-6720-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.325262463441187, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1860672303978511092, 'z1': {'__RealLiteral__': 0, 'data': '1.29274022286411566435418517821', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21596590
{'Lhash': '1638742919452871267742973288549', 'Lhash_array': ['1638742919452871267742973288549'], 'label': '2-6720-1.1-c1-0-69', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6720/2/a/v'}
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id: 24576341
{'Lhash': '1638742919452871267742973288549', 'Lhash_array': ['1638742919452871267742973288549'], 'label': '2-6720-1.1-c1-0-69', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6720/2/a/v/1/1'}
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id: 27236
{'Lhash': '1860672303978511092', 'Lhash_array': ['1860672303978511092'], 'label': '2-6720-1.1-c1-0-69', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6720/v'}