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lfunc_lfunctions • Show schema
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{'Lhash': '1155665296928903834828451454526', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': -2, 'a5': -1, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.4734924879256983, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [5, [1, 1]], [29, [1, -1]]], 'bad_primes': [3, 5, 29], 'central_character': '435.1', 'coefficient_field': '1.1.1.1', 'conductor': 435, 'conductor_radical': 435, 'degree': 2, 'euler_factors': [[1, 0, 2], [1, 1], [1, 1], [1, 2, 7], [1, -1, 11], [1, -6, 13], [1, -4, 17], [1, 2, 19], [1, -3, 23], [1, -1], [1, 4, 31], [1, 3, 37], [1, -7, 41], [1, -5, 43], [1, -6, 47], [1, -13, 53], [1, 0, 59], [1, 0, 61], [1, 10, 67], [1, -6, 71], [1, -3, 73], [1, 0, 79], [1, -9, 83], [1, 10, 89], [1, -17, 97], [1, 3, 101], [1, 6, 103], [1, -12, 107], [1, -11, 109], [1, 12, 113]], 'euler_factors_factorization': [[[[1, 0, 2], 1]], [[[1, 1], 1]], [[[1, 1], 1]], [[[1, 2, 7], 1]], [[[1, -1, 11], 1]], [[[1, -6, 13], 1]], [[[1, -4, 17], 1]], [[[1, 2, 19], 1]], [[[1, -3, 23], 1]], [[[1, -1], 1]], [[[1, 4, 31], 1]], [[[1, 3, 37], 1]], [[[1, -7, 41], 1]], [[[1, -5, 43], 1]], [[[1, -6, 47], 1]], [[[1, -13, 53], 1]], [[[1, 0, 59], 1]], [[[1, 0, 61], 1]], [[[1, 10, 67], 1]], [[[1, -6, 71], 1]], [[[1, -3, 73], 1]], [[[1, 0, 79], 1]], [[[1, -9, 83], 1]], [[[1, 10, 89], 1]], [[[1, -17, 97], 1]], [[[1, 3, 101], 1]], [[[1, 6, 103], 1]], [[[1, -12, 107], 1]], [[[1, -11, 109], 1]], [[[1, 12, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-435-1.1-c1-0-1', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/435/2/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.809496527650355, 0.7996127903996118, 0.7683426044207848, 0.7111194438420544, 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'0.911659172267844473526681142024', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.43182364531126383498212067183', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.16721175306965324518809801959', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.4734924879256983, 'bad_primes': [3, 5, 29], 'central_character': '1.1', 'conductor': 435, 'conductor_radical': 435, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, -2, -1, 0, -2, 0, 1, 0, 1, 2, 6, 0, 1, 4, 4, 0, -2, 2, 2, 0, 3, 0, 1, 0, -1, 4, 1, 0, -4, 0, -1, 0, 2, -2, -3, 0, -6, 0, 7, 0, 5, -2, -1, 0, 6, -4, -3, 0, -4, -12, 13, 0, -1, 0, 2, 0, 0, -2, 0, 0, -2, -8, -6, 0, -10, -8, -3, 0, 6, 0, 3, 0, -1, 4, -2, 0, 0, -4, 1, 0, 9, -4, -4, 0, -1, 0, -10, 0, -12, -6, 4, 0, 2, 0, 17, 0, 1, -2], 'euler11': [1, -1, 11], 'euler13': [1, -6, 13], 'euler17': [1, -4, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 2], 'euler23': [1, -3, 23], 'euler29': [1, -1, 0], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 3, 37], 'euler41': [1, -7, 41], 'euler43': [1, -5, 43], 'euler47': [1, -6, 47], 'euler5': [1, 1, 0], 'euler53': [1, -13, 53], 'euler59': [1, 0, 59], 'euler61': [1, 0, 61], 'euler67': [1, 10, 67], 'euler7': [1, 2, 7], 'euler71': [1, -6, 71], 'euler73': [1, -3, 73], 'euler79': [1, 0, 79], 'euler83': [1, -9, 83], 'euler89': [1, 10, 89], 'euler97': [1, -17, 97], 'euler_factors': [[1, 0, 2], [1, 1, 0], [1, 1, 0], [1, 2, 7], [1, -1, 11], [1, -6, 13], [1, -4, 17], [1, 2, 19], [1, -3, 23], [1, -1, 0], [1, 4, 31], [1, 3, 37], [1, -7, 41], [1, -5, 43], [1, -6, 47], [1, -13, 53], [1, 0, 59], [1, 0, 61], [1, 10, 67], [1, -6, 71], [1, -3, 73], [1, 0, 79], [1, -9, 83], [1, 10, 89], [1, -17, 97]], 'index': 1, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/435/b', 'ModularForm/GL2/Q/holomorphic/435/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/435/2/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': '2-435-1.1-c1-0-1', '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': '2-435-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.8637307981373539, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2001060445599230482, 'z1': {'__RealLiteral__': 0, 'data': '0.911659172267844473526681142024', 'prec': 107}}
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lfunc_instances • Show schema
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id: 10755155
{'Lhash': '1155665296928903834828451454526', 'Lhash_array': ['1155665296928903834828451454526'], 'factors': ['2-435-1.1-c1-0-1'], 'label': '2-435-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/435/2/a/b'}
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id: 24549338
{'Lhash': '1155665296928903834828451454526', 'Lhash_array': ['1155665296928903834828451454526'], 'factors': ['2-435-1.1-c1-0-1'], 'label': '2-435-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/435/2/a/b/1/1'}
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id: 97203
{'Lhash': '2001060445599230482', 'Lhash_array': ['2001060445599230482'], 'factors': ['2-435-1.1-c1-0-1'], 'label': '2-435-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/435/b'}