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lfunc_lfunctions • Show schema
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{'Lhash': '1358334144686638485867287942611', 'a10': [0, 0], 'a2': [0, -49679.43713211717], 'a3': [0, -15522124.385220557], 'a4': [6121888118.236017, 0], 'a5': [0, 0], 'a6': [-771130402552.4677, 0], 'a7': [0, 122168353210676.02], 'a8': [0, -730875071432023.9], 'a9': [5318124221125264.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 172.4570722025188, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '16.5', 'prec': 14}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]]], 'bad_primes': [5], 'central_character': '25.24', 'coefficient_field': 'CDF', 'conductor': 25, 'conductor_radical': 5, 'conjugate': '1020163979685891182805725066544', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 49679.43713211717], [-8589934592.0, 0]], [[1.0, 0], [0, 15522124.385220557], [-5559060566555523.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -122168353210676.02], [-7730993719707444000000000000, 0]], [[1.0, 0], [-215762684013593860, 0], [23225154419887806000000000000000000, 0]], [[1.0, 0], [0, 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'10.42971163212276633867932130911666', '11.31176630123104991851672265781292'], 'prelabel': '2-5e2-5.4-c33-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.132291201558044, 'root_angle': 0.35241638234956674, 'root_number': '0.44721359549995793928183473374625524708812367192230514486 + 0.89442719099991587856366946749251049417624734384461028971*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.17620819117478337', 'prec': 64}, 'spectral_label': 'c33-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07153670297011045903868857601', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.74554174370435379989627101769', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.60001395140453920284843399498', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 172.4570722025188, 'bad_primes': [5], 'central_character': '5.4', 'conductor': 25, 'conductor_radical': 5, 'degree': 2, 'index': 35, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/25/34/b/a/24/2'], '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': '2-5e2-5.4-c33-0-35', 'motivic_weight': 33, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [33], 'order_of_vanishing': 0, 'prelabel': '2-5e2-5.4-c33-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.132291201558044, 'root_angle': 0.17620819117478337, 'self_dual': False, 'spectral_label': 'c33-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07153670297011045903868857601', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1358334144686638485867287942611', 'Lhash_array': ['1358334144686638485867287942611'], 'label': '2-5e2-5.4-c33-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/25/34/b/a/24/2'}