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lfunc_lfunctions • Show schema
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{'Lhash': '1625205828022614610628354886263', 'a10': [0.5739779522395382, 6.814199419208251e-62], 'a2': [0.6427876096865394, 1.1133407984528387], 'a3': [0.0, 0.0], 'a4': [0.17364817766693036, -0.3007674663608706], 'a5': [0.22323779409789932, -0.38665920154716127], 'a6': [0.0, 0.0], 'a7': [1.7660444431189781, 3.058878703906754], 'a8': [3.017626026941956, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.244', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '1997627765938449242233222023116', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6427876096865394, -1.1133407984528387], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.22323779409789932, 0.38665920154716127], [-2.5, -4.330127018922194]], [[1.0, 0], [-1.7660444431189781, 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'10.40324236031735321070997655529704'], 'prelabel': '2-3e6-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.3333333333333333, 'root_number': '0.5000000000000001 - 0.8660254037844386*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.166666666667', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28206134066438379642344795401', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.58991793415285694948798626767', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.64940731605354518447549802817', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '9.4', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/c/c/244/5'], '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': '2-3e6-9.4-c1-0-15', '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': '2-3e6-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.16666666666666666, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28206134066438379642344795401', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1625205828022614610628354886263', 'Lhash_array': ['1625205828022614610628354886263'], 'label': '2-3e6-9.4-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/c/c/244/5'}