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lfunc_lfunctions • Show schema
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{'Lhash': '2145848505342011762788354312506', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.0387109578734, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, -1]], [23, [1, -1]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '2760.1', 'coefficient_field': '1.1.1.1', 'conductor': 2760, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -1], [1, 3, 7], [1, 4, 11], [1, 0, 13], [1, -3, 17], [1, 4, 19], [1, -1], [1, -1, 29], [1, -1, 31], [1, -1, 37], [1, -3, 41], [1, 12, 43], [1, 10, 47], [1, 9, 53], [1, 9, 59], [1, 10, 61], [1, -1, 67], [1, -5, 71], [1, 0, 73], [1, -4, 79], [1, 9, 83], [1, 8, 89], [1, 10, 97], [1, 15, 101], [1, 0, 103], [1, -11, 107], [1, 0, 109], [1, 9, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, -1], 1]], [[[1, 3, 7], 1]], [[[1, 4, 11], 1]], [[[1, 0, 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1.1316189724948638, 1.0084242562304535, 0.8122059438762202, 0.5652625727271006, 0.2915178048792971, 0.015077508180952654, -0.24120077055001934, -0.4570446249616235, -0.6159338427452941, -0.7060312411011014], 'positive_zeros': ['1.69277599439125458601956379486790', '2.83876560427255664873171575295754', '3.26938362309098050357401997412973', '4.48451466655585348753334838956612', '5.35087007376937847803643361018777', '6.25698405456036687653312464825714', '6.83151970081810399317257118224838', '7.85995167596304103889604675592394', '8.340435800291842829296369118143314'], 'prelabel': '2-2760-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.694540548112605, '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': 492053923657933549, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.69277599439125458601956379487', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.83876560427255664873171575296', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.26938362309098050357401997413', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.0387109578734, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 2760, 'conductor_radical': 690, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, -3, 0, 1, 0, -4, 0, 0, 0, 1, 0, 3, 0, -4, 0, -3, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, -4, 0, -3, 0, 1, 0, 0, 0, 3, 0, -12, 0, 1, 0, -10, 0, 2, 0, 3, 0, -9, 0, -4, 0, -4, 0, -9, 0, -10, 0, -3, 0, 0, 0, 1, 0, 1, 0, 5, 0, 0, 0, 1, 0, 12, 0, 4, 0, 1, 0, -9, 0, 3, 0, 1, 0, -8, 0, 0, 0, 1, 0, -4, 0, -10, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, 0, 13], 'euler17': [1, -3, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, -1, 29], 'euler3': [1, -1, 0], 'euler31': [1, -1, 31], 'euler37': [1, -1, 37], 'euler41': [1, -3, 41], 'euler43': [1, 12, 43], 'euler47': [1, 10, 47], 'euler5': [1, -1, 0], 'euler53': [1, 9, 53], 'euler59': [1, 9, 59], 'euler61': [1, 10, 61], 'euler67': [1, -1, 67], 'euler7': [1, 3, 7], 'euler71': [1, -5, 71], 'euler73': [1, 0, 73], 'euler79': [1, -4, 79], 'euler83': [1, 9, 83], 'euler89': [1, 8, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -1, 0], [1, 3, 7], [1, 4, 11], [1, 0, 13], [1, -3, 17], [1, 4, 19], [1, -1, 0], [1, -1, 29], [1, -1, 31], [1, -1, 37], [1, -3, 41], [1, 12, 43], [1, 10, 47], [1, 9, 53], [1, 9, 59], [1, 10, 61], [1, -1, 67], [1, -5, 71], [1, 0, 73], [1, -4, 79], [1, 9, 83], [1, 8, 89], [1, 10, 97]], 'index': 40, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2760/j', 'ModularForm/GL2/Q/holomorphic/2760/2/a/j/1/1', 'ModularForm/GL2/Q/holomorphic/2760/2/a/j'], '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': '2-2760-1.1-c1-0-40', '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': '2-2760-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.694540548112605, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 492053923657933549, 'z1': {'__RealLiteral__': 0, 'data': '1.69277599439125458601956379487', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20222088
{'Lhash': '2145848505342011762788354312506', 'Lhash_array': ['2145848505342011762788354312506'], 'label': '2-2760-1.1-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2760/2/a/j'}
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id: 24558664
{'Lhash': '2145848505342011762788354312506', 'Lhash_array': ['2145848505342011762788354312506'], 'label': '2-2760-1.1-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2760/2/a/j/1/1'}
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id: 102456
{'Lhash': '492053923657933549', 'Lhash_array': ['492053923657933549'], 'label': '2-2760-1.1-c1-0-40', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2760/j'}