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lfunc_lfunctions • Show schema
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{'Lhash': '1230196370221333141073771168572', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.5, 0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [7.793693946769586, 4.499691298148977], 'a6': [0.0, 0.0], 'a7': [-6.974026176572677, -0.6024606945511847], 'a8': [0.0, 0.0], 'a9': [1.5, -2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.577668441252989, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.5, -0.8660254037844386]]], [7, [[1.0, 0], [6.974026176572677, 0.6024606945511847]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.145', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': '2594203450087313361194687899306', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.5, -0.8660254037844386]], [[1.0, 0], [-7.793693946769586, -4.499691298148977], [12.5, 21.650635094610966]], [[1.0, 0], [6.974026176572677, 0.6024606945511847]], 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'12.65232614339331842144840713974303'], 'prelabel': '2-168-7.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1395486536307113, 'root_angle': -0.21611228000313362, 'root_number': '0.21131761795042753 - 0.9774174463062122*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.216112280003', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.970453822212403832767519869345', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.82430819470137303186868442035', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.01436583029365228578744391573', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.577668441252989, 'bad_primes': [2, 3, 7], 'central_character': '7.5', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/3/z/a/145/4'], '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': '2-168-7.5-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-168-7.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1395486536307113, 'root_angle': -0.21611228000313362, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.970453822212403832767519869345', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1230196370221333141073771168572', 'Lhash_array': ['1230196370221333141073771168572'], 'factors': ['2-168-7.5-c2-0-1'], 'label': '2-168-7.5-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/3/z/a/145/4'}