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lfunc_lfunctions • Show schema
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{'Lhash': '1786126473094408986770180700921', 'a10': [1.6784851267052199, 1.4773921887668697], 'a2': [0.7071067811865476, -0.7071067811865476], 'a3': [1.731480990344251, -0.044424993826586025], 'a4': [0.0, -1.0], 'a5': [0.14219418006493298, 2.2315422503631117], 'a6': [1.1929287353790694, -1.2557551641569682], 'a7': [2.343826868759448, 2.343826868759448], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [2.9960528398470156, -0.1538420646137888], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.426087387979079, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [3, [[1.0, 0], [-1.731480990344251, 0.044424993826586025]]], [5, [[1.0, 0], [-0.14219418006493298, -2.2315422503631117]]], [31, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '930.497', 'coefficient_field': 'CDF', 'conductor': 930, 'conductor_radical': 930, 'conjugate': 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0.02268564349289878, 'root_number': '0.9898586324867161 + 0.14205593156052423*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0226856434929', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40900534640446866025593633050', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.65545659559590415387867340472', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.26376530240167239541139640026', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.426087387979079, 'bad_primes': [2, 3, 5, 31], 'central_character': '15.2', 'conductor': 930, 'conductor_radical': 930, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/930/2/j/g/497/20'], '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': '2-930-15.2-c1-0-34', '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': '2-930-15.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7250848405103056, 'root_angle': 0.02268564349289878, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40900534640446866025593633050', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1786126473094408986770180700921', 'Lhash_array': ['1786126473094408986770180700921'], 'factors': ['2-930-15.2-c1-0-34'], 'label': '2-930-15.2-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/930/2/j/g/497/20'}