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lfunc_lfunctions • Show schema
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{'Lhash': '2823500898065171259269501748679', 'a10': [1.1752184489322965, 0.6785126878476759], 'a2': [-0.20401144537981153, 0.11778606290779882], 'a3': [0.0, 0.0], 'a4': [-1.97225288676936, 3.4160422052589197], 'a5': [-2.880275777528983, -4.9887839864901515], 'a6': [0.0, 0.0], 'a7': [1.9445057735387203, 0.0], 'a8': [0.0, -1.8715041136268051], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.6594125205610775, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-17.818137547952997, 6.596512284702242]]]], 'bad_primes': [3, 19], 'central_character': '171.145', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '306277551663536859276892716858', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.20401144537981153, -0.11778606290779882], [2.0, -3.4641016151377544]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.880275777528983, 4.9887839864901515], [-12.5, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-171-19.12-c2-0-11', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/171/3/p/c/145/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.39735509922817985, 0.5902934053345178, 0.7754229769892355, 0.9524953177784559, 1.120204219237368, 1.2760126563706187, 1.4161047988565976, 1.5354650855861123, 1.628079769636755, 1.687252888335239, 1.706026233057169, 1.677689630493776, 1.5963626007635614, 1.4576211341826208, 1.2591346253560254, 1.0012691077826552, 0.6876052705726226, 0.3253147954706078, -0.074662271448462, -0.4976919175861599, -0.9258145181119963, -1.338432249822129, -1.713317419901216, -2.0279151931015083, -2.2608825296791064, -2.393772756420124, -2.4127452973006864, -2.3101563086879637, 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'11.73868528310491390978038298765130', '12.90901141687025967138010985356976'], 'prelabel': '2-171-19.12-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.158567237905986, 'root_angle': 0.7516310641431463, 'root_number': '-0.7107207956957798 + 0.7034742003553205*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.375815532072', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.22734947434003077963034926984', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.05993930815258456710308967975', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.29969493777412332492728414974', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.6594125205610775, 'bad_primes': [3, 19], 'central_character': '19.12', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/3/p/c/145/2'], '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': '2-171-19.12-c2-0-11', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-171-19.12-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.158567237905986, 'root_angle': 0.37581553207157314, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.22734947434003077963034926984', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2823500898065171259269501748679', 'Lhash_array': ['2823500898065171259269501748679'], 'label': '2-171-19.12-c2-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/3/p/c/145/2'}