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lfunc_lfunctions • Show schema
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{'Lhash': '2465293300983194460107090457350', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.223226574724038, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [23, [1, 1]]], 'bad_primes': [2, 3, 23], 'central_character': '1656.1', 'coefficient_field': '1.1.1.1', 'conductor': 1656, 'conductor_radical': 138, 'degree': 2, 'euler_factors': [[1], [1], [1, 0, 5], [1, -4, 7], [1, 6, 11], [1, 2, 13], [1, 6, 17], [1, 6, 19], [1, 1], [1, -6, 29], [1, 0, 31], [1, 8, 37], [1, 6, 41], [1, 2, 43], [1, -8, 47], [1, -8, 53], [1, 4, 59], [1, 4, 61], [1, -2, 67], [1, -8, 71], [1, -6, 73], [1, -12, 79], [1, 10, 83], [1, 10, 89], [1, 18, 97], [1, 6, 101], [1, -8, 103], [1, 2, 107], [1, 12, 109], [1, 2, 113]], 'euler_factors_factorization': [[1], [1], [[[1, 0, 5], 1]], [[[1, -4, 7], 1]], [[[1, 6, 11], 1]], [[[1, 2, 13], 1]], [[[1, 6, 17], 1]], [[[1, 6, 19], 1]], [[[1, 1], 1]], [[[1, -6, 29], 1]], [[[1, 0, 31], 1]], [[[1, 8, 37], 1]], [[[1, 6, 41], 1]], [[[1, 2, 43], 1]], [[[1, -8, 47], 1]], [[[1, -8, 53], 1]], [[[1, 4, 59], 1]], [[[1, 4, 61], 1]], [[[1, -2, 67], 1]], [[[1, -8, 71], 1]], [[[1, -6, 73], 1]], [[[1, -12, 79], 1]], [[[1, 10, 83], 1]], [[[1, 10, 89], 1]], [[[1, 18, 97], 1]], [[[1, 6, 101], 1]], [[[1, -8, 103], 1]], [[[1, 2, 107], 1]], [[[1, 12, 109], 1]], [[[1, 2, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-1656-1.1-c1-0-27', '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/1656/2/a/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.448795744377047e-60, 0.151156693068033, 0.302366223788151, 0.4536433269422688, 0.6049284665558196, 0.7560553806963698, 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0.9819634583838026, 1.5061863584287214, 2.001618221785759, 2.446458658125747, 2.8213968075203404, 3.1105624273864825, 3.302312862749193], 'positive_zeros': ['1.94477350504889909491080153121133', '2.53210728436057851679498975052873', '4.14218283371488576671439383743574', '4.86456749161076388512551590669260', '5.46759063803448033131660005497477', '6.64787884445607472888119813091129', '7.51799242171937345337021049954106', '8.320236055459786854807713491348262', '8.601348166683304914056585059265487'], 'prelabel': '2-1656-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.6363754721871113, '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': 717446676828261975, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.94477350504889909491080153121', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.53210728436057851679498975053', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.14218283371488576671439383744', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.223226574724038, 'bad_primes': [2, 3, 23], 'central_character': '1.1', 'conductor': 1656, 'conductor_radical': 138, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 4, 0, 0, 0, -6, 0, -2, 0, 0, 0, -6, 0, -6, 0, 0, 0, -1, 0, -5, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -6, 0, -2, 0, 0, 0, 8, 0, 9, 0, 0, 0, 8, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 8, 0, 6, 0, 0, 0, -24, 0, 12, 0, 0, 0, -10, 0, 0, 0, 0, 0, -10, 0, -8, 0, 0, 0, 0, 0, -18, 0, 0, 0], 'euler11': [1, 6, 11], 'euler13': [1, 2, 13], 'euler17': [1, 6, 17], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 0, 31], 'euler37': [1, 8, 37], 'euler41': [1, 6, 41], 'euler43': [1, 2, 43], 'euler47': [1, -8, 47], 'euler5': [1, 0, 5], 'euler53': [1, -8, 53], 'euler59': [1, 4, 59], 'euler61': [1, 4, 61], 'euler67': [1, -2, 67], 'euler7': [1, -4, 7], 'euler71': [1, -8, 71], 'euler73': [1, -6, 73], 'euler79': [1, -12, 79], 'euler83': [1, 10, 83], 'euler89': [1, 10, 89], 'euler97': [1, 18, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 5], [1, -4, 7], [1, 6, 11], [1, 2, 13], [1, 6, 17], [1, 6, 19], [1, 1, 0], [1, -6, 29], [1, 0, 31], [1, 8, 37], [1, 6, 41], [1, 2, 43], [1, -8, 47], [1, -8, 53], [1, 4, 59], [1, 4, 61], [1, -2, 67], [1, -8, 71], [1, -6, 73], [1, -12, 79], [1, 10, 83], [1, 10, 89], [1, 18, 97]], 'index': 27, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1656/e', 'ModularForm/GL2/Q/holomorphic/1656/2/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/1656/2/a/e'], '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': '2-1656-1.1-c1-0-27', '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': '2-1656-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.6363754721871113, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 717446676828261975, 'z1': {'__RealLiteral__': 0, 'data': '1.94477350504889909491080153121', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20644008
{'Lhash': '2465293300983194460107090457350', 'Lhash_array': ['2465293300983194460107090457350'], 'label': '2-1656-1.1-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1656/2/a/e'}
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id: 24553980
{'Lhash': '2465293300983194460107090457350', 'Lhash_array': ['2465293300983194460107090457350'], 'label': '2-1656-1.1-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1656/2/a/e/1/1'}
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id: 40993
{'Lhash': '717446676828261975', 'Lhash_array': ['717446676828261975'], 'label': '2-1656-1.1-c1-0-27', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1656/e'}