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lfunc_lfunctions • Show schema
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{'Lhash': '1338157346130254366809707872560', 'a10': [0.0, 0.0], 'a2': [-2.114907541476756, 0.0], 'a3': [1.0, 0.0], 'a4': [2.4728339089952556, 0.0], 'a5': [0.0, 0.0], 'a6': [-2.114907541476756, 0.0], 'a7': [-5.1149075414767555, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 35.333802894416586, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [59, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 59], 'central_character': '4425.1', 'coefficient_field': 'CDF', 'conductor': 4425, 'conductor_radical': 885, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.114907541476756, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.1149075414767555, 0], [7.0, 0]], [[1.0, 0], [4.587741450472011, 0], [11.0, 0]], [[1.0, 0], [-2.5877414504720115, 0], [13.0, 0]], [[1.0, 0], [2.188686644032255, 0], [17.0, 0]], [[1.0, 0], [-0.5271660910047444, 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'6.24662792703790980199577693045584', '6.75312941092329636085435303853380', '7.42302861821341378264613737555218', '8.262257040385384260673979186953965'], 'prelabel': '2-4425-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.944224330761465, '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': '1.05562001539645927867492300210', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.54512362031839136224242614360', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.89570991874184602495455526681', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 35.333802894416586, 'bad_primes': [3, 5, 59], 'central_character': '1.1', 'conductor': 4425, 'conductor_radical': 885, 'degree': 2, 'index': 86, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4425/2/a/w/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': '2-4425-1.1-c1-0-86', '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': '2-4425-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.944224330761465, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05562001539645927867492300210', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1338157346130254366809707872560', 'Lhash_array': ['1338157346130254366809707872560'], 'label': '2-4425-1.1-c1-0-86', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4425/2/a/w/1/1'}