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lfunc_lfunctions • Show schema
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{'Lhash': '1173004327550459166724391994060', 'a10': [0.35689586789220945, 0.0], 'a2': [-1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-0.35689586789220945, 0.0], 'a6': [-1.0, 0.0], 'a7': [-4.048917339522306, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.096830764957835, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 13], 'central_character': '1014.1', 'coefficient_field': 'CDF', 'conductor': 1014, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.35689586789220945, 0], [5.0, 0]], [[1.0, 0], [4.048917339522306, 0], [7.0, 0]], [[1.0, 0], [-0.9118539999795806, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.0978346790446105, 0], [17.0, 0]], [[1.0, 0], [-4.987918414869868, 0], [19.0, 0]], [[1.0, 0], 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[[1.0, 0], [-12.987918414869869, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-1014-1.1-c1-0-2', 'leading_term': '1.187794774943747546602198532270', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1014/2/a/m/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.1877947749437476, 1.1841948070397263, 1.1732984015669679, 1.1548224480378995, 1.1283159322741374, 1.093189593877932, 1.0487545168670729, 0.9942672652621439, 0.9289791001180452, 0.8521869724365921, 0.7632842848536677, 0.661809760162207, 0.5474930741112732, 0.4202961617424966, 0.28044927819655213, 0.1284809952695329, -0.034758635073478907, -0.2080824944743099, -0.3899591105432957, -0.5785143481176324, -0.7715426862969972, -0.9665285730294243, -1.1606781876219017, 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'6.00421437108238013889510175074773', '6.77834408758778658600133648615854', '7.43477749687803727867578798689913', '8.515946485045853002081019226148942', '9.135311224362448943950807052588344', '9.870824776878324751252205154114968'], 'prelabel': '2-1014-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.845493061836179, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.925337255659619455615447351878', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.69595240870254514358033529224', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.27963387769484010305639416499', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.096830764957835, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 1014, 'conductor_radical': 78, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1014/2/a/m/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': '2-1014-1.1-c1-0-2', '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': '2-1014-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.845493061836179, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.925337255659619455615447351878', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1173004327550459166724391994060', 'Lhash_array': ['1173004327550459166724391994060'], 'label': '2-1014-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1014/2/a/m/1/2'}