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lfunc_lfunctions • Show schema
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{'Lhash': '1924290036147480854846003694689', 'a10': [-1.467041009225093, -9.203973503028352e-61], 'a2': [-0.25881904510252074, 0.9659258262890683], 'a3': [0.0, -1.0], 'a4': [-0.8660254037844386, -0.5], 'a5': [0.37969815313387695, 1.4170527990356967], 'a6': [0.9659258262890683, 0.25881904510252074], 'a7': [1.636974886152442, -2.07853631724495], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.25881904510252074, -0.9659258262890683]]], [3, [[1.0, 0], [0, 1.0]]], [7, [[1.0, 0], [-1.636974886152442, 2.07853631724495]]], [13, [[1.0, 0], [3.503650870603428, -0.8511348758685913]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.397', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '1228546904492462361560349146538', 'degree': 2, 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'4.29960278519754200168290869905270', '4.90686586883680068113238005263235', '6.00117598371332728865609887894597', '7.48501514023508200037224746471031', '8.633191148409600824780088532017084', '9.046836055782810163259984285908886', '10.01976331215566421890673478561854', '10.69863105913270271259098346528203'], 'prelabel': '2-546-91.33-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.08529416702090305, 'root_number': '0.9643131475401968 + 0.2647643357424082*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0426470835105', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51799717982307527564874727593', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.78986004377686387329115723110', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.29960278519754200168290869905', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '91.33', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/by/a/397/3'], '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': '2-546-91.33-c1-0-12', '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': '2-546-91.33-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.042647083510451524, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51799717982307527564874727593', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1924290036147480854846003694689', 'Lhash_array': ['1924290036147480854846003694689'], 'label': '2-546-91.33-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/by/a/397/3'}