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lfunc_lfunctions • Show schema
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{'Lhash': '693857161244500973319311015057', 'a10': [9.001739965613522, 4.335009492544828], 'a2': [-1.4405797809117693, -1.806429908502186], 'a3': [-0.13382962331973777, 0.06444894983535787], 'a4': [-0.7428770412467864, 3.2547569792814457], 'a5': [-3.8959960023817417, 1.8762127897226426], 'a6': [0.30921475999559994, 0.1489099801745425], 'a7': [-1.2122677032519882, -2.3516817419991485], 'a8': [2.7862678026320955, -1.3417958549482418], 'a9': [-1.8567127046331782, 2.328244090044452], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [1.2122677032519882, 2.3516817419991485]]], [13, [[1.0, 0], [-0.6234898018587335, -0.7818314824680298]]]], 'bad_primes': [7, 13], 'central_character': '637.547', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '692200913624412616653008412910', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.54735678831341858799055656126', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07246668364845813222964612038', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.56967714759398424683758704422', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '49.8', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/w/b/547/3'], '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': '2-637-49.8-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': '2-637-49.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.185231144673655, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.54735678831341858799055656126', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '693857161244500973319311015057', 'Lhash_array': ['693857161244500973319311015057'], 'label': '2-637-49.8-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/w/b/547/3'}