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lfunc_lfunctions • Show schema
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{'Lhash': '362459857834347414969400671622', 'a10': [4.711344058824678, 3.7571715127818957], 'a2': [-0.53449511094231, -2.3417760896360442], 'a3': [2.0062299713299208, 0.457908899081992], 'a4': [-3.396292494565013, 1.6355682634290165], 'a5': [-1.9614261359864058, 1.564185147707598], 'a6': [-4.013784808279598e-61, -4.942891444987915], 'a7': [0.0, 1.3273448380661348], 'a8': [2.6501923440357755, 3.3232360865982136], 'a9': [1.112371534296715, 0.5356898976012864], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.837064387755599, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [2.0815962214240744, -3.559066896105356]]], [43, [[1.0, 0], [-4.744637929837724, 4.526412587772485]]]], 'bad_primes': [17, 43], 'central_character': '731.16', 'coefficient_field': 'CDF', 'conductor': 731, 'conductor_radical': 731, 'conjugate': '2548382702277222793701808113443', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.53449511094231, 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{'__RealLiteral__': 0, 'data': '-0.149466478733', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.28593041155748254942641955154', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49645464177916315314460182208', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.27329093522944571239412052219', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.837064387755599, 'bad_primes': [17, 43], 'central_character': '731.16', 'conductor': 731, 'conductor_radical': 731, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/731/2/p/a/16/6'], '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': '2-731-731.16-c1-0-6', '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': '2-731-731.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.416001735875949, 'root_angle': -0.14946647873275914, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.28593041155748254942641955154', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '362459857834347414969400671622', 'Lhash_array': ['362459857834347414969400671622'], 'label': '2-731-731.16-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/731/2/p/a/16/6'}