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lfunc_lfunctions • Show schema
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{'Lhash': '2044036486202274842693422526298', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.7071067811865476, 0.7071067811865476], 'a4': [0, 0], 'a5': [1.9791709289161015, -1.0406163722205104], 'a6': [0, 0], 'a7': [-0.7981153005909988, 0.7981153005909988], 'a8': [0, 0], 'a9': [0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.852174775958158, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [5, [[1.0, 0], [-1.9791709289161015, 1.0406163722205104]]], [31, [[1.0, 0], [5.269622381077329, -1.7975205035962458]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '1860.433', 'coefficient_field': 'CDF', 'conductor': 1860, 'conductor_radical': 930, 'conjugate': '387074416905035689776100084494', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-1.9791709289161015, 1.0406163722205104]], 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'root_angle': 0.33374383727090556, 'root_number': '-0.5022320497057779084737470732255964154513850875650337588 + 0.8647328883813388465300566418666502440019946379243849353*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.33374383727090556', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.61246047281030273960887649958', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.37521324752741389871917748990', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.58346631228874802169089083703', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.852174775958158, 'bad_primes': [2, 3, 5, 31], 'central_character': '155.123', 'conductor': 1860, 'conductor_radical': 930, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1860/2/s/a/433/1'], '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': '2-1860-155.123-c1-0-25', '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': '2-1860-155.123-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8538519400669973, 'root_angle': 0.33374383727090556, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.61246047281030273960887649958', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2044036486202274842693422526298', 'Lhash_array': ['2044036486202274842693422526298'], 'factors': ['2-1860-155.123-c1-0-25'], 'label': '2-1860-155.123-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1860/2/s/a/433/1'}