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lfunc_lfunctions • Show schema
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{'Lhash': '2220602006040853923480185964915', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -2, '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, -1, 3], [1, 1], [1], [1, 5, 11], [1, -7, 13], [1, 3, 17], [1, 2, 19], [1, -8, 23], [1, 5, 29], [1, 10, 31], [1, -4, 37], [1, 6, 41], [1, -2, 43], [1, 7, 47], [1, 10, 53], [1, 10, 59], [1, 12, 61], [1, 2, 67], [1, 0, 71], [1, 2, 73], [1, 7, 79], [1, -4, 83], [1, 8, 89], [1, -17, 97], [1, -10, 101], [1, -1, 103], [1, -2, 107], [1, -13, 109], [1, 12, 113]], 'euler_factors_factorization': [[1], [[[1, -1, 3], 1]], [[[1, 1], 1]], [1], [[[1, 5, 11], 1]], [[[1, -7, 13], 1]], [[[1, 3, 17], 1]], 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-2.2381814970482528, -1.6497334122335048, -1.127693030090623, -0.6883850331385905, -0.3434163765677569, -0.0991677362826877, 0.043444328913845844, 0.08892169147595491, 0.04685735579301872], 'positive_zeros': ['1.75174610862098275150537555723211', '2.98880939986356079200127451473246', '3.52125752483082004986811543715909', '4.68433049548119319480718263070741', '5.59495571406520217607287420944623', '6.37665734327720103607362555321249', '7.47724546913021809652464850473361', '8.049248252417975821764082579322035', '8.853083512708142125385087195760364'], 'prelabel': '2-1960-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.9560938811118933, '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': 494838220842754859, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.75174610862098275150537555723', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.98880939986356079200127451473', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52125752483082004986811543716', '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, 1, 0, -1, 0, 0, 0, -2, 0, -5, 0, 7, 0, -1, 0, -3, 0, -2, 0, 0, 0, 8, 0, 1, 0, -5, 0, -5, 0, -10, 0, -5, 0, 0, 0, 4, 0, 7, 0, -6, 0, 2, 0, 2, 0, -7, 0, 0, 0, -3, 0, -10, 0, 5, 0, -2, 0, -10, 0, -12, 0, 0, 0, -7, 0, -2, 0, 8, 0, 0, 0, -2, 0, 1, 0, 0, 0, -7, 0, 1, 0, 4, 0, 3, 0, -5, 0, -8, 0, 0, 0, -10, 0, 2, 0, 17, 0, 10, 0], 'euler11': [1, 5, 11], 'euler13': [1, -7, 13], 'euler17': [1, 3, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, 5, 29], 'euler3': [1, -1, 3], 'euler31': [1, 10, 31], 'euler37': [1, -4, 37], 'euler41': [1, 6, 41], 'euler43': [1, -2, 43], 'euler47': [1, 7, 47], 'euler5': [1, 1, 0], 'euler53': [1, 10, 53], 'euler59': [1, 10, 59], 'euler61': [1, 12, 61], 'euler67': [1, 2, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, 2, 73], 'euler79': [1, 7, 79], 'euler83': [1, -4, 83], 'euler89': [1, 8, 89], 'euler97': [1, -17, 97], 'euler_factors': [[1, 0, 0], [1, -1, 3], [1, 1, 0], [1, 0, 0], [1, 5, 11], [1, -7, 13], [1, 3, 17], [1, 2, 19], [1, -8, 23], [1, 5, 29], [1, 10, 31], [1, -4, 37], [1, 6, 41], [1, -2, 43], [1, 7, 47], [1, 10, 53], [1, 10, 59], [1, 12, 61], [1, 2, 67], [1, 0, 71], [1, 2, 73], [1, 7, 79], [1, -4, 83], [1, 8, 89], [1, -17, 97]], 'index': 32, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1960/h', 'ModularForm/GL2/Q/holomorphic/1960/2/a/h/1/1', 'ModularForm/GL2/Q/holomorphic/1960/2/a/h'], '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-c1-0-32', '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': '2-1960-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.9560938811118933, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 494838220842754859, 'z1': {'__RealLiteral__': 0, 'data': '1.75174610862098275150537555723', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20609173
{'Lhash': '2220602006040853923480185964915', 'Lhash_array': ['2220602006040853923480185964915'], 'label': '2-1960-1.1-c1-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1960/2/a/h'}
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id: 24555269
{'Lhash': '2220602006040853923480185964915', 'Lhash_array': ['2220602006040853923480185964915'], 'label': '2-1960-1.1-c1-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1960/2/a/h/1/1'}
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id: 103383
{'Lhash': '494838220842754859', 'Lhash_array': ['494838220842754859'], 'label': '2-1960-1.1-c1-0-32', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1960/h'}