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lfunc_lfunctions • Show schema
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{'Lhash': '1819523745597749485486675495563', 'a10': [1.0238933791896907, 0.0], 'a2': [-0.6568749007631732, 0.0], 'a3': [2.678269510580956, 0.0], 'a4': [-1.5685153647473713, 0.0], 'a5': [-1.5587342095125059, 0.0], 'a6': [-1.759288018979898, 0.0], 'a7': [2.176070422237499, 0.0], 'a8': [2.3440681760902886, 0.0], 'a9': [4.173127571307552, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.217971201457601, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[13, [[1.0, 0], [-1.0, 0]]], [31, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [13, 31], 'central_character': '403.1', 'coefficient_field': 'CDF', 'conductor': 403, 'conductor_radical': 403, 'conjugate': '1819523745597749485486675495563', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6568749007631732, 0], [2.0, 0]], [[1.0, 0], [-2.678269510580956, 0], [3.0, 0]], [[1.0, 0], [1.5587342095125059, 0], [5.0, 0]], [[1.0, 0], [-2.176070422237499, 0], [7.0, 0]], [[1.0, 0], [-0.877965929559642, 0], 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'5.13343666530974458056769437165652', '7.11485570698157016764496732035898', '8.021691756039554883601111958677740', '8.398888122566616187779623380333587', '9.196447252286113706924079638041435', '10.03799722306106010357211264362114', '11.10831147642673978429636224579944'], 'prelabel': '2-403-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7938704528080063, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.43535114902336665308837251587', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.17711986111718680614910518331', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.09393056291002306566429244527', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.217971201457601, 'bad_primes': [13, 31], 'central_character': '1.1', 'conductor': 403, 'conductor_radical': 403, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/403/2/a/e/1/4'], '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': '2-403-1.1-c1-0-7', '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': '2-403-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7938704528080063, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43535114902336665308837251587', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1819523745597749485486675495563', 'Lhash_array': ['1819523745597749485486675495563'], 'label': '2-403-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/403/2/a/e/1/4'}