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lfunc_lfunctions • Show schema
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{'Lhash': '1949471096430095035731480566893', 'a10': [0.6180339887498949, 0.0], 'a2': [1.0, 0.0], 'a3': [-2.23606797749979, 0.0], 'a4': [1.0, 0.0], 'a5': [0.6180339887498949, 0.0], 'a6': [-2.23606797749979, 0.0], 'a7': [2.8541019662496847, 0.0], 'a8': [1.0, 0.0], 'a9': [2.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.715214849384736, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 11, 19], 'central_character': '4598.1', 'coefficient_field': 'CDF', 'conductor': 4598, 'conductor_radical': 418, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.23606797749979, 0], [3.0, 0]], [[1.0, 0], [-0.6180339887498949, 0], [5.0, 0]], [[1.0, 0], [-2.8541019662496847, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.618033988749895, 0], [13.0, 0]], [[1.0, 0], [6.23606797749979, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], 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'6.13418160963120084366446820014950', '7.18980898680577379130674501175558', '7.57241471340565279441833351710081'], 'prelabel': '2-4598-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.059308116392889, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.53786153383204316574314039475', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.21750881400812327202680498540', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.67542164100473162127555079968', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.715214849384736, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 4598, 'conductor_radical': 418, 'degree': 2, 'index': 136, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4598/2/a/bi/1/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-4598-1.1-c1-0-136', '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': '2-4598-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.059308116392889, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.53786153383204316574314039475', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1949471096430095035731480566893', 'Lhash_array': ['1949471096430095035731480566893'], 'label': '2-4598-1.1-c1-0-136', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4598/2/a/bi/1/1'}