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lfunc_lfunctions • Show schema
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{'Lhash': '1672451583010759337560785853899', 'a10': [0.0, 0.0], 'a2': [-0.3111078174659819, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.9032119259115532, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [2.688892182534018, 0.0], 'a8': [1.2143197433775352, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 34.13604686409738, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 19], 'central_character': '4275.1', 'coefficient_field': 'CDF', 'conductor': 4275, 'conductor_radical': 285, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.3111078174659819, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.688892182534018, 0], [7.0, 0]], [[1.0, 0], [-0.21431974337753518, 0], [11.0, 0]], [[1.0, 0], [3.1175316692890886, 0], [13.0, 0]], [[1.0, 0], [0.4745724391564829, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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'6.63635463843122343156185068410870', '7.55522140109057753411488453732902', '8.102128579928093780819093489024539'], 'prelabel': '2-4275-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.842606170545588, 'root_angle': 0.5, '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': '1.31933166971218177959031336761', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.30031809092734832419211003213', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52605344301102520749554057516', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 34.13604686409738, 'bad_primes': [3, 5, 19], 'central_character': '1.1', 'conductor': 4275, 'conductor_radical': 285, 'degree': 2, 'index': 102, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4275/2/a/bd/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': '2-4275-1.1-c1-0-102', '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': '2-4275-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.842606170545588, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.31933166971218177959031336761', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1672451583010759337560785853899', 'Lhash_array': ['1672451583010759337560785853899'], 'factors': ['2-4275-1.1-c1-0-102'], 'label': '2-4275-1.1-c1-0-102', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4275/2/a/bd/1/2'}