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lfunc_lfunctions • Show schema
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{'Lhash': '2155167850836030041102087207857', 'a10': [0.0, 0.0], 'a2': [1.3228756555322954, 0.5], 'a3': [0.0, 0.0], 'a4': [1.5, 1.3228756555322954], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 2.6457513110645907], 'a8': [1.3228756555322954, 2.5], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.0122301309362665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.3228756555322954, -0.5]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, -2.6457513110645907]]]], 'bad_primes': [2, 3, 7], 'central_character': '252.55', 'coefficient_field': 'CDF', 'conductor': 252, 'conductor_radical': 42, 'conjugate': '3085093293096308426552861938779', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3228756555322954, -0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-5.0, 0]], [[1.0, 0], [0, -2.6457513110645907]], [[1.0, 0], [0, 4.0], [-11.0, 0]], [[1.0, 0], [0, 0], [-13.0, 0]], [[1.0, 0], [0, 0], [-17.0, 0]], [[1.0, 0], 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'rational': False, 'root_analytic_conductor': 1.4185309763753016, 'root_angle': -0.26994654383738415, 'root_number': '0.6614378277661476 - 0.7500000000000001*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.134973271919', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70012766171373320250956563777', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.44127348092956702547536900357', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.46865325691232563849339806941', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.0122301309362665, 'bad_primes': [2, 3, 7], 'central_character': '28.27', 'conductor': 252, 'conductor_radical': 42, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/252/2/b/c/55/4'], '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': '2-252-28.27-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': '2-252-28.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4185309763753016, 'root_angle': -0.13497327191869207, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.70012766171373320250956563777', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2155167850836030041102087207857', 'Lhash_array': ['2155167850836030041102087207857'], 'label': '2-252-28.27-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/252/2/b/c/55/4'}