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lfunc_lfunctions • Show schema
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{'Lhash': '3862060064099360323292753682428', 'a10': [-2.8541019662496847, 0.0], 'a2': [1.0, 0.0], 'a3': [0.6180339887498949, 0.0], 'a4': [1.0, 0.0], 'a5': [-2.8541019662496847, 0.0], 'a6': [0.6180339887498949, 0.0], 'a7': [1.2360679774997898, 0.0], 'a8': [1.0, 0.0], 'a9': [-2.618033988749895, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [37, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 37], 'central_character': '74.1', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '3862060064099360323292753682428', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.6180339887498949, 0], [3.0, 0]], [[1.0, 0], [2.8541019662496847, 0], [5.0, 0]], [[1.0, 0], [-1.2360679774997898, 0], [7.0, 0]], [[1.0, 0], [3.618033988749895, 0], [11.0, 0]], [[1.0, 0], [-3.8541019662496847, 0], [13.0, 0]], [[1.0, 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'8.350653004117880787826262769278797', '10.49717959069935234629396118610245', '11.48124010159742978757620231312557', '12.35190252318154107531529859447920', '13.64492861912870423155420813297077', '14.55568504382690214010878001480773'], 'prelabel': '2-74-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.04662819818334026192895002349', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.44392201551849548294070730841', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.01796754899817048898544080092', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'bad_primes': [2, 37], 'central_character': '1.1', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/2/a/b/1/2'], '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': '2-74-1.1-c1-0-3', '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': '2-74-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.04662819818334026192895002349', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3862060064099360323292753682428', 'Lhash_array': ['3862060064099360323292753682428'], 'label': '2-74-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/2/a/b/1/2'}