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lfunc_lfunctions • Show schema
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{'Lhash': '1207446256342336170418403131993', 'a10': [0, 0], 'a2': [0.8660254037844386, 0.5], 'a3': [0, 0], 'a4': [0.5, 0.8660254037844386], 'a5': [0, 0], 'a6': [0, 0], 'a7': [2.343247043607996, -1.2284922843153654], 'a8': [0, 1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.152876636703333, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.343247043607996, 1.2284922843153654]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '3150.1601', 'coefficient_field': 'CDF', 'conductor': 3150, 'conductor_radical': 210, 'conjugate': '1467553413610568567212991586802', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.343247043607996, 1.2284922843153654]], [[1.0, 0], [-2.03985613151733, 1.177711486639639], [5.5, 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'8.730901496082647157888909113755239'], 'prelabel': '2-3150-21.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.015264363590751, 'root_angle': -0.2507777014062305, 'root_number': '0.70537705427552351784874022254864985418849451601379556405 - 0.7088322871466741738916104750178560421867149918411420370*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.12538885070311526', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.952507146783937178262348253080', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.07854064124657217364919855209', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.87263111054360904000098397416', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.152876636703333, 'bad_primes': [2, 3, 5, 7], 'central_character': '21.5', 'conductor': 3150, 'conductor_radical': 210, 'degree': 2, 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3150/2/bf/d/1601/11'], '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': '2-3150-21.5-c1-0-32', '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': '2-3150-21.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.015264363590751, 'root_angle': -0.12538885070311526, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.952507146783937178262348253080', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1207446256342336170418403131993', 'Lhash_array': ['1207446256342336170418403131993'], 'label': '2-3150-21.5-c1-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3150/2/bf/d/1601/11'}