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lfunc_lfunctions • Show schema
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{'Lhash': '1297057979172050570889340658883', 'a10': [1.0, 0.0], 'a2': [1.0, 0.0], 'a3': [0.38492266446475554, 0.0], 'a4': [1.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.38492266446475554, 0.0], 'a7': [0.9510908488209392, 0.0], 'a8': [1.0, 0.0], 'a9': [-2.8518345423813534, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.76924015606564, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [-1.0, 0]]], [43, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 11, 43], 'central_character': '4730.1', 'coefficient_field': 'CDF', 'conductor': 4730, 'conductor_radical': 4730, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.38492266446475554, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.9510908488209392, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.3202593104866146, 0], [13.0, 0]], [[1.0, 0], [-7.41568550777568, 0], [17.0, 0]], [[1.0, 0], 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'3.62472261512117629901030010762738', '4.69749190060381745598994613748880', '5.41880572208193204425307517595346', '5.89801000426091410132740732456048', '6.75106735449229234753238152735873', '7.53229692659077734792561545225880', '8.276271462670720935237581517829995'], 'prelabel': '2-4730-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.145668405964126, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.02319833157380008975803505010', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.12244228778325131825156845245', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.01012385417195106350432608870', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 37.76924015606564, 'bad_primes': [2, 5, 11, 43], 'central_character': '1.1', 'conductor': 4730, 'conductor_radical': 4730, 'degree': 2, 'index': 68, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4730/2/a/bd/1/6'], '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': '2-4730-1.1-c1-0-68', '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': '2-4730-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.145668405964126, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.02319833157380008975803505010', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1297057979172050570889340658883', 'Lhash_array': ['1297057979172050570889340658883'], 'label': '2-4730-1.1-c1-0-68', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4730/2/a/bd/1/6'}