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lfunc_lfunctions • Show schema
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{'Lhash': '1032505069299112468627006996112', 'a10': [-6.854101966249685, 0.0], 'a2': [1.618033988749895, 0.0], 'a3': [1.0, 0.0], 'a4': [0.6180339887498949, 0.0], 'a5': [-4.23606797749979, 0.0], 'a6': [1.618033988749895, 0.0], 'a7': [-1.0, 0.0], 'a8': [-2.23606797749979, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.289987153607356, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7, 11], 'central_character': '2541.1', 'coefficient_field': 'CDF', 'conductor': 2541, 'conductor_radical': 231, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.618033988749895, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.23606797749979, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-6.23606797749979, 0], [13.0, 0]], [[1.0, 0], [4.47213595499958, 0], [17.0, 0]], [[1.0, 0], [-3.0, 0], [19.0, 0]], [[1.0, 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'6.66498985060980633707361761410146', '7.24857412388667026438192650924597', '8.170794739156512386351255390664095', '8.857143704386704643850720887221839'], 'prelabel': '2-2541-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.504440825852567, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.814502883612581387160443608813', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.79248104188882076909598089751', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43870567717536772254314128943', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.289987153607356, 'bad_primes': [3, 7, 11], 'central_character': '1.1', 'conductor': 2541, 'conductor_radical': 231, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2541/2/a/ba/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': '2-2541-1.1-c1-0-27', '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': '2-2541-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.504440825852567, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.814502883612581387160443608813', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1032505069299112468627006996112', 'Lhash_array': ['1032505069299112468627006996112'], 'label': '2-2541-1.1-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2541/2/a/ba/1/2'}