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lfunc_lfunctions • Show schema
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{'Lhash': '3251491262760798411050136400988', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.5, 0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.5, -0.8660254037844386], 'a8': [0.0, 0.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.041921461061172206, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.5, -0.8660254037844386]]], [7, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [2, 3, 7], 'central_character': '84.53', 'coefficient_field': 'CDF', 'conductor': 84, 'conductor_radical': 42, 'conjugate': '4463195604100378182409895449883', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], 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'6.30895696473354994681334896900283', '7.44725460239841168931737259170251', '8.796010299104171695587299127571593', '10.11348932277312344731628512468072', '11.57081641310592920438165715556923', '12.27926998190461195602564601841589', '13.20498120399190008275121892140565', '14.33197631703146060715751911730401'], 'prelabel': '2-84-21.11-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.20474731026602574, 'root_angle': -0.14649371361272057, 'root_number': '0.89595321966310477774725020770463 - 0.44414843034206066891807967048929*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07324685680636027', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.56497434085969418732679777437', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.07920460323713432335456360487', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.30895696473354994681334896900', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.041921461061172206, 'bad_primes': [2, 3, 7], 'central_character': '21.11', 'conductor': 84, 'conductor_radical': 42, 'degree': 2, 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/84/1/p/a/53/1', 'ArtinRepresentation/2.84.6t5.b.a'], 'is_instance_Artin': True, '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': '2-84-21.11-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-84-21.11-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.20474731026602574, 'root_angle': -0.07324685680636028, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.56497434085969418732679777437', 'prec': 103}}
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lfunc_instances • Show schema
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id: 19804961
{'Lhash': '3251491262760798411050136400988', 'Lhash_array': ['3251491262760798411050136400988'], 'label': '2-84-21.11-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/84/1/p/a/53/1'}
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id: 24596370
{'Lhash': '3251491262760798411050136400988', 'Lhash_array': ['3251491262760798411050136400988'], 'label': '2-84-21.11-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.84.6t5.b.a'}