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lfunc_lfunctions • Show schema
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{'Lhash': '1433818235427013463670545215851', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [7.543720269382876, 13.06610678465832], 'a6': [0, 0], 'a7': [-16.291903693676417, 8.807603194738777], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 59.473925285786564, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [16.291903693676417, -8.807603194738777]]]], 'bad_primes': [2, 3, 7], 'central_character': '1008.17', 'coefficient_field': 'CDF', 'conductor': 1008, 'conductor_radical': 42, 'conjugate': '257707174929849334167619262793', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-7.543720269382876, -13.06610678465832], [-62.5, 108.25317547305482]], [[1.0, 0], [16.291903693676417, -8.807603194738777]], [[1.0, 0], [8.56528996184363, 4.945172465157619], [665.5, 1152.6798124370878]], [[1.0, 0], [0, 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'8.382385956039919155583350344477407', '9.009062090271730999320084419865908', '9.808280329919996473742396511628699'], 'prelabel': '2-1008-21.17-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.711933952374499, 'root_angle': 0.49781070182837167, 'root_number': '0.0068778288259415671296855727510024193749904296113620952 + 0.9999763474555990953037577847422978940464480913472013234*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.24890535091418584', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13108315112134765924231403713', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.21632304431702596510494852634', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.61118741938061576141615408759', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 59.473925285786564, 'bad_primes': [2, 3, 7], 'central_character': '21.17', 'conductor': 1008, 'conductor_radical': 42, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1008/4/bt/a/17/8'], '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': '2-1008-21.17-c3-0-36', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-1008-21.17-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.711933952374499, 'root_angle': 0.24890535091418584, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.13108315112134765924231403713', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1433818235427013463670545215851', 'Lhash_array': ['1433818235427013463670545215851'], 'label': '2-1008-21.17-c3-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1008/4/bt/a/17/8'}