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lfunc_lfunctions • Show schema
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{'Lhash': '1542428843410747227900137801874', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.650678796170963, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '1960.1', 'coefficient_field': '1.1.1.1', 'conductor': 1960, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[1], [1, -3, 3], [1, 1], [1], [1, 5, 11], [1, -5, 13], [1, -7, 17], [1, -2, 19], [1, 2, 23], [1, -7, 29], [1, 4, 31], [1, 6, 37], [1, -12, 41], [1, 2, 43], [1, 1, 47], [1, 0, 53], [1, -4, 59], [1, 4, 61], [1, -8, 67], [1, 0, 71], [1, 6, 73], [1, 3, 79], [1, -4, 83], [1, 0, 89], [1, 13, 97], [1, -18, 101], [1, 13, 103], [1, -18, 107], [1, -5, 109], [1, -6, 113]], 'euler_factors_factorization': [[1], [[[1, -3, 3], 1]], [[[1, 1], 1]], [1], [[[1, 5, 11], 1]], [[[1, -5, 13], 1]], [[[1, -7, 17], 1]], [[[1, -2, 19], 1]], [[[1, 2, 23], 1]], [[[1, -7, 29], 1]], [[[1, 4, 31], 1]], [[[1, 6, 37], 1]], [[[1, -12, 41], 1]], [[[1, 2, 43], 1]], [[[1, 1, 47], 1]], [[[1, 0, 53], 1]], [[[1, -4, 59], 1]], [[[1, 4, 61], 1]], [[[1, -8, 67], 1]], [[[1, 0, 71], 1]], [[[1, 6, 73], 1]], [[[1, 3, 79], 1]], [[[1, -4, 83], 1]], [[[1, 0, 89], 1]], [[[1, 13, 97], 1]], [[[1, -18, 101], 1]], [[[1, 13, 103], 1]], [[[1, -18, 107], 1]], [[[1, -5, 109], 1]], [[[1, -6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-1960-1.1-c1-0-17', 'leading_term': '3.19750926488800773595096345853000000000000000000000000000000000000000000000000000000000000', '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/1960/2/a/o', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': 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0.3210990706149009, 0.6834706678022245, 0.9238453951754564, 1.0409348255087592, 1.0393103588989616, 0.9289922735273105, 0.7247793589440799, 0.4453557713059674, 0.11222289306880864, -0.2514873268860373, -0.6222552969291523, -0.9774081641893192], 'positive_zeros': ['1.21676181365200032832887757199628', '2.50550432047388901594073309744465', '3.28269243130114732472876126998448', '3.84714819358078169724331248538149', '5.01872075614464181579565790111195', '5.99774302994776081413912070293434', '7.29927337271737671794138924215670', '7.79995782949092071026536073407994', '8.332265077163568720704999874857088', '8.937999621329745000322771267529578'], 'prelabel': '2-1960-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.9560938811118933, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1650450958279113649, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21676181365200032832887757200', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.50550432047388901594073309744', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.28269243130114732472876126998', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.650678796170963, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 1960, 'conductor_radical': 70, 'degree': 2, 'dirichlet_coefficients': [1, 0, 3, 0, -1, 0, 0, 0, 6, 0, -5, 0, 5, 0, -3, 0, 7, 0, 2, 0, 0, 0, -2, 0, 1, 0, 9, 0, 7, 0, -4, 0, -15, 0, 0, 0, -6, 0, 15, 0, 12, 0, -2, 0, -6, 0, -1, 0, 0, 0, 21, 0, 0, 0, 5, 0, 6, 0, 4, 0, -4, 0, 0, 0, -5, 0, 8, 0, -6, 0, 0, 0, -6, 0, 3, 0, 0, 0, -3, 0, 9, 0, 4, 0, -7, 0, 21, 0, 0, 0, 0, 0, -12, 0, -2, 0, -13, 0, -30, 0], 'euler11': [1, 5, 11], 'euler13': [1, -5, 13], 'euler17': [1, -7, 17], 'euler19': [1, -2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 2, 23], 'euler29': [1, -7, 29], 'euler3': [1, -3, 3], 'euler31': [1, 4, 31], 'euler37': [1, 6, 37], 'euler41': [1, -12, 41], 'euler43': [1, 2, 43], 'euler47': [1, 1, 47], 'euler5': [1, 1, 0], 'euler53': [1, 0, 53], 'euler59': [1, -4, 59], 'euler61': [1, 4, 61], 'euler67': [1, -8, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, 6, 73], 'euler79': [1, 3, 79], 'euler83': [1, -4, 83], 'euler89': [1, 0, 89], 'euler97': [1, 13, 97], 'euler_factors': [[1, 0, 0], [1, -3, 3], [1, 1, 0], [1, 0, 0], [1, 5, 11], [1, -5, 13], [1, -7, 17], [1, -2, 19], [1, 2, 23], [1, -7, 29], [1, 4, 31], [1, 6, 37], [1, -12, 41], [1, 2, 43], [1, 1, 47], [1, 0, 53], [1, -4, 59], [1, 4, 61], [1, -8, 67], [1, 0, 71], [1, 6, 73], [1, 3, 79], [1, -4, 83], [1, 0, 89], [1, 13, 97]], 'index': 17, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1960/o', 'ModularForm/GL2/Q/holomorphic/1960/2/a/o/1/1', 'ModularForm/GL2/Q/holomorphic/1960/2/a/o'], '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': '2-1960-1.1-c1-0-17', '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': '2-1960-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.9560938811118933, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1650450958279113649, 'z1': {'__RealLiteral__': 0, 'data': '1.21676181365200032832887757200', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20609166
{'Lhash': '1542428843410747227900137801874', 'Lhash_array': ['1542428843410747227900137801874'], 'label': '2-1960-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1960/2/a/o'}
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id: 24555276
{'Lhash': '1542428843410747227900137801874', 'Lhash_array': ['1542428843410747227900137801874'], 'label': '2-1960-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1960/2/a/o/1/1'}
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id: 87631
{'Lhash': '1650450958279113649', 'Lhash_array': ['1650450958279113649'], 'label': '2-1960-1.1-c1-0-17', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1960/o'}