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lfunc_lfunctions • Show schema
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{'Lhash': '5627949715728515801040090865943', 'a10': [0.0, 0.0], 'a2': [0.0, -2.5779354745735183], 'a3': [0.0, 0.0], 'a4': [-4.645751311064591, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [2.6457513110645907, 0.0], 'a8': [0.0, 6.820576161692803], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5030575327340666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.6457513110645907, 0]]]], 'bad_primes': [3, 7], 'central_character': '63.62', 'coefficient_field': 'CDF', 'conductor': 63, 'conductor_radical': 21, 'conjugate': '2384867763120469166509465767123', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.5779354745735183], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [5.0, 0]], [[1.0, 0], [-2.6457513110645907, 0]], [[1.0, 0], [0, -0.9132302620277513], [-11.0, 0]], [[1.0, 0], [0, 0], [-13.0, 0]], [[1.0, 0], [0, 0], [17.0, 0]], [[1.0, 0], [0, 0], [-19.0, 0]], [[1.0, 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'root_analytic_conductor': 0.7092654881876508, 'root_angle': 0.3479566380076518, 'root_number': '-0.5773502691896257 + 0.816496580927726*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.347956638008', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.43966950728793303655486985089', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.64820847737513046977322495616', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.97782560947259423579006266016', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5030575327340666, 'bad_primes': [3, 7], 'central_character': '21.20', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/63/2/c/a/62/1'], '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': '2-63-21.20-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': '2-63-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7092654881876508, 'root_angle': 0.3479566380076518, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '4.43966950728793303655486985089', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5627949715728515801040090865943', 'Lhash_array': ['5627949715728515801040090865943'], 'factors': ['2-63-21.20-c1-0-3'], 'label': '2-63-21.20-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/2/c/a/62/1'}