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lfunc_lfunctions • Show schema
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{'Lhash': '1347159125030588937341950646590', '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, -6, 13], [1, -6, 17], [1, -4, 19], [1, 4, 23], [1, -2, 29], [1, -8, 31], [1, 6, 37], [1, -6, 41], [1, 8, 43], [1, 0, 47], [1, 6, 53], [1, -4, 59], [1, 10, 61], [1, 8, 67], [1, -12, 71], [1, 14, 73], [1, 16, 79], [1, -12, 83], [1, -14, 89], [1, -18, 97], [1, 14, 101], [1, 8, 103], [1, 4, 107], [1, -2, 109], [1, -2, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, 1], 1]], [[[1, -1], 1]], [[[1, -4, 11], 1]], [[[1, 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0.24227571987924715, -0.18388806070439742, -0.5248662199609534, -0.7682331386400709, -0.9074733807132767, -0.9423233807029304, -0.8787680700446919, -0.7286902139814261, -0.5091893019272143, -0.24160519036891048, 0.04970168570346445, 0.3387477811874156, 0.5994253894258335, 0.8070205344718562], 'positive_zeros': ['1.06272116684837661219445451654576', '1.56329332733124901721570301294432', '2.99905083226437049353669993941136', '3.57783277762029035141233456022012', '4.15868508279290697812095254590432', '5.06425614930114652546490156983708', '6.03607354837694609771547977606053', '6.51360879286623148980464582375900', '7.50597799504879283586560785170365', '7.994728824495080514825983230938310'], 'prelabel': '2-6720-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.325262463441187, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 317837118677107409, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06272116684837661219445451655', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.56329332733124901721570301294', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99905083226437049353669993941', '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, 6, 0, -1, 0, 6, 0, 4, 0, 1, 0, -4, 0, 1, 0, 1, 0, 2, 0, 8, 0, 4, 0, -1, 0, -6, 0, 6, 0, 6, 0, -8, 0, -1, 0, 0, 0, 1, 0, 6, 0, -6, 0, -4, 0, 4, 0, 4, 0, -10, 0, 1, 0, -6, 0, -8, 0, -4, 0, 12, 0, -14, 0, 1, 0, 4, 0, -16, 0, 1, 0, 12, 0, -6, 0, 2, 0, 14, 0, 6, 0, 8, 0, -4, 0, 18, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, -6, 13], 'euler17': [1, -6, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, -2, 29], 'euler3': [1, -1, 0], 'euler31': [1, -8, 31], 'euler37': [1, 6, 37], 'euler41': [1, -6, 41], 'euler43': [1, 8, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, 6, 53], 'euler59': [1, -4, 59], 'euler61': [1, 10, 61], 'euler67': [1, 8, 67], 'euler7': [1, -1, 0], 'euler71': [1, -12, 71], 'euler73': [1, 14, 73], 'euler79': [1, 16, 79], 'euler83': [1, -12, 83], 'euler89': [1, -14, 89], 'euler97': [1, -18, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 1, 0], [1, -1, 0], [1, -4, 11], [1, -6, 13], [1, -6, 17], [1, -4, 19], [1, 4, 23], [1, -2, 29], [1, -8, 31], [1, 6, 37], [1, -6, 41], [1, 8, 43], [1, 0, 47], [1, 6, 53], [1, -4, 59], [1, 10, 61], [1, 8, 67], [1, -12, 71], [1, 14, 73], [1, 16, 79], [1, -12, 83], [1, -14, 89], [1, -18, 97]], 'index': 53, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6720/bx', 'ModularForm/GL2/Q/holomorphic/6720/2/a/bx/1/1', 'ModularForm/GL2/Q/holomorphic/6720/2/a/bx'], '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-c1-0-53', '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': '2-6720-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.325262463441187, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 317837118677107409, 'z1': {'__RealLiteral__': 0, 'data': '1.06272116684837661219445451655', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21704550
{'Lhash': '1347159125030588937341950646590', 'Lhash_array': ['1347159125030588937341950646590'], 'label': '2-6720-1.1-c1-0-53', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6720/2/a/bx'}
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id: 24576369
{'Lhash': '1347159125030588937341950646590', 'Lhash_array': ['1347159125030588937341950646590'], 'label': '2-6720-1.1-c1-0-53', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6720/2/a/bx/1/1'}
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id: 98243
{'Lhash': '317837118677107409', 'Lhash_array': ['317837118677107409'], 'label': '2-6720-1.1-c1-0-53', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6720/bx'}