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lfunc_lfunctions • Show schema
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{'Lhash': '2744061737059759415177192116556', 'a10': [2.4208893899136004, 0.0], 'a2': [0.7201706136355333, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.4813542872558194, 0.0], 'a5': [3.3615498106658013, 0.0], 'a6': [0.0, 0.0], 'a7': [0.45152791177985396, 0.0], 'a8': [-2.507169053335718, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.707938911053704, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [149, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 149], 'central_character': '1341.1', 'coefficient_field': 'CDF', 'conductor': 1341, 'conductor_radical': 447, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7201706136355333, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.3615498106658013, 0], [5.0, 0]], [[1.0, 0], [-0.45152791177985396, 0], [7.0, 0]], [[1.0, 0], [5.217710075904674, 0], [11.0, 0]], [[1.0, 0], [5.1631276768985375, 0], [13.0, 0]], [[1.0, 0], [7.125982618410435, 0], [17.0, 0]], [[1.0, 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['2.16468302587930389000777193168629', '2.71268641267436813445848240771453', '4.38221863299898151259524952395738', '4.95582937805243594151900890561015', '5.72833483057947295609683320479753', '6.42574606910644023461879571386568', '7.63904839074778235925342075186761', '8.500109718307398974416765202536782', '9.367509409696202539750700933946683'], 'prelabel': '2-1341-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.272298719715806, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.16468302587930389000777193169', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.71268641267436813445848240771', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.38221863299898151259524952396', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.707938911053704, 'bad_primes': [3, 149], 'central_character': '1.1', 'conductor': 1341, 'conductor_radical': 447, 'degree': 2, 'index': 55, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1341/2/a/d/1/7'], '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': '2-1341-1.1-c1-0-55', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1341-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.272298719715806, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.16468302587930389000777193169', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2744061737059759415177192116556', 'Lhash_array': ['2744061737059759415177192116556'], 'label': '2-1341-1.1-c1-0-55', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1341/2/a/d/1/7'}