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lfunc_lfunctions • Show schema
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{'Lhash': '1973147798443548409836743905584', 'a10': [1.5, -2.598076211353316], 'a2': [0.8660254037844386, 0.5], 'a3': [-0.5, 0.8660254037844386], 'a4': [0.5, 0.8660254037844386], 'a5': [0.0, -3.0], 'a6': [-0.8660254037844386, 0.5], 'a7': [0.8660254037844386, -0.5], 'a8': [0.0, 1.0], 'a9': [1.0, 1.7320508075688772], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.6989435883192785, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 13], 'central_character': '338.147', 'coefficient_field': 'CDF', 'conductor': 338, 'conductor_radical': 26, 'conjugate': '2116947300183539297050848426196', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0.5, -0.8660254037844386], [-1.5, -2.598076211353316]], [[1.0, 0], [0, 3.0], [-5.0, 0]], [[1.0, 0], [-0.8660254037844386, 0.5], [3.5, -6.06217782649107]], [[1.0, 0], 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3.298574332420038, 3.741485648690838, 3.51827187707033, 2.6607066145768807, 1.379749094068129], 'positive_zeros': ['1.55653915841502414727331083641918', '3.18528608724977792782108047105159', '4.06627112795307223189785650987902', '5.85189780807458816715704525488776', '6.49148667943659092833895167287690', '7.22580839930106836723591290574393', '8.697849266539438259622865848174853', '9.850147166656173589126068592679474', '10.84531898189319695833100174547353', '11.62011912322396610554581162090301'], 'prelabel': '2-338-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6428461852283307, 'root_angle': -0.1912489445961322, 'root_number': '0.8248687808030644 - 0.5653242383415611*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0956244722981', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55653915841502414727331083642', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.18528608724977792782108047105', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.06627112795307223189785650988', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.6989435883192785, 'bad_primes': [2, 13], 'central_character': '13.4', 'conductor': 338, 'conductor_radical': 26, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/338/2/e/a/147/2'], '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': '2-338-13.4-c1-0-8', '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': '2-338-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6428461852283307, 'root_angle': -0.0956244722980661, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55653915841502414727331083642', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1973147798443548409836743905584', 'Lhash_array': ['1973147798443548409836743905584'], 'label': '2-338-13.4-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/338/2/e/a/147/2'}