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lfunc_lfunctions • Show schema
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{'Lhash': '2000737906556250658302784077523', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.549044428938494, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -1]], [19, [1, 1]]], 'bad_primes': [2, 5, 19], 'central_character': '6080.1', 'coefficient_field': '1.1.1.1', 'conductor': 6080, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[1], [1, -2, 3], [1, -1], [1, 2, 7], [1, 0, 11], [1, 6, 13], [1, -2, 17], [1, 1], [1, -2, 23], [1, -2, 29], [1, 4, 31], [1, -10, 37], [1, 10, 41], [1, -6, 43], [1, -6, 47], [1, 6, 53], [1, 4, 59], [1, 2, 61], [1, 2, 67], [1, 12, 71], [1, 6, 73], [1, 8, 79], [1, 2, 83], [1, -2, 89], [1, 18, 97], [1, -10, 101], [1, -6, 103], [1, 18, 107], [1, 10, 109], [1, 10, 113]], 'euler_factors_factorization': [[1], [[[1, -2, 3], 1]], [[[1, -1], 1]], [[[1, 2, 7], 1]], [[[1, 0, 11], 1]], [[[1, 6, 13], 1]], [[[1, -2, 17], 1]], [[[1, 1], 1]], [[[1, -2, 23], 1]], [[[1, -2, 29], 1]], [[[1, 4, 31], 1]], [[[1, -10, 37], 1]], [[[1, 10, 41], 1]], [[[1, -6, 43], 1]], [[[1, -6, 47], 1]], [[[1, 6, 53], 1]], [[[1, 4, 59], 1]], [[[1, 2, 61], 1]], [[[1, 2, 67], 1]], [[[1, 12, 71], 1]], [[[1, 6, 73], 1]], [[[1, 8, 79], 1]], [[[1, 2, 83], 1]], [[[1, -2, 89], 1]], [[[1, 18, 97], 1]], [[[1, -10, 101], 1]], [[[1, -6, 103], 1]], [[[1, 18, 107], 1]], [[[1, 10, 109], 1]], [[[1, 10, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 130, 'label': '2-6080-1.1-c1-0-130', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/6080/2/a/v', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.5423840600792556e-60, 0.2524248658084447, 0.5039585358116786, 0.7536614077672027, 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4.565710190551908, 3.7442818286406894, 2.8594163922742384, 1.947327498964016, 1.0446989703319671, 0.18699285772925925, -0.5931759243600667, -1.2675172477249461, -1.8133218669673543, -2.2144333017463538], 'positive_zeros': ['1.57830391607595602459925925121161', '2.69748101374550081075014095448240', '2.84733050783303684181265239875217', '3.89511864614255116875710510303855', '4.76015239441290460184897269323876', '5.59465419717945855450175289517191', '6.35527884347965566169530376204642', '7.23436546772269163480377177671491', '7.65919107683087884298823480656978'], 'prelabel': '2-6080-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.967714433653154, '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': 498923592003963697, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.57830391607595602459925925121', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.69748101374550081075014095448', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.84733050783303684181265239875', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.549044428938494, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 6080, 'conductor_radical': 190, 'degree': 2, 'dirichlet_coefficients': [1, 0, 2, 0, 1, 0, -2, 0, 1, 0, 0, 0, -6, 0, 2, 0, 2, 0, -1, 0, -4, 0, 2, 0, 1, 0, -4, 0, 2, 0, -4, 0, 0, 0, -2, 0, 10, 0, -12, 0, -10, 0, 6, 0, 1, 0, 6, 0, -3, 0, 4, 0, -6, 0, 0, 0, -2, 0, -4, 0, -2, 0, -2, 0, -6, 0, -2, 0, 4, 0, -12, 0, -6, 0, 2, 0, 0, 0, -8, 0, -11, 0, -2, 0, 2, 0, 4, 0, 2, 0, 12, 0, -8, 0, -1, 0, -18, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 6, 13], 'euler17': [1, -2, 17], 'euler19': [1, 1, 0], 'euler2': [1, 0, 0], 'euler23': [1, -2, 23], 'euler29': [1, -2, 29], 'euler3': [1, -2, 3], 'euler31': [1, 4, 31], 'euler37': [1, -10, 37], 'euler41': [1, 10, 41], 'euler43': [1, -6, 43], 'euler47': [1, -6, 47], 'euler5': [1, -1, 0], 'euler53': [1, 6, 53], 'euler59': [1, 4, 59], 'euler61': [1, 2, 61], 'euler67': [1, 2, 67], 'euler7': [1, 2, 7], 'euler71': [1, 12, 71], 'euler73': [1, 6, 73], 'euler79': [1, 8, 79], 'euler83': [1, 2, 83], 'euler89': [1, -2, 89], 'euler97': [1, 18, 97], 'euler_factors': [[1, 0, 0], [1, -2, 3], [1, -1, 0], [1, 2, 7], [1, 0, 11], [1, 6, 13], [1, -2, 17], [1, 1, 0], [1, -2, 23], [1, -2, 29], [1, 4, 31], [1, -10, 37], [1, 10, 41], [1, -6, 43], [1, -6, 47], [1, 6, 53], [1, 4, 59], [1, 2, 61], [1, 2, 67], [1, 12, 71], [1, 6, 73], [1, 8, 79], [1, 2, 83], [1, -2, 89], [1, 18, 97]], 'index': 130, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6080/v', 'ModularForm/GL2/Q/holomorphic/6080/2/a/v/1/1', 'ModularForm/GL2/Q/holomorphic/6080/2/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': '2-6080-1.1-c1-0-130', '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': '2-6080-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.967714433653154, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 498923592003963697, 'z1': {'__RealLiteral__': 0, 'data': '1.57830391607595602459925925121', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21669873
{'Lhash': '2000737906556250658302784077523', 'Lhash_array': ['2000737906556250658302784077523'], 'label': '2-6080-1.1-c1-0-130', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6080/2/a/v'}
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id: 24573387
{'Lhash': '2000737906556250658302784077523', 'Lhash_array': ['2000737906556250658302784077523'], 'label': '2-6080-1.1-c1-0-130', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6080/2/a/v/1/1'}
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id: 34055
{'Lhash': '498923592003963697', 'Lhash_array': ['498923592003963697'], 'label': '2-6080-1.1-c1-0-130', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6080/v'}