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lfunc_lfunctions • Show schema
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{'Lhash': '952789154584260173266526469478', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-2.768734305276283, 0], 'a6': [0, 0], 'a7': [0.4809009198615832, 2.6016791318831545], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.19568209498026, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.4809009198615832, -2.6016791318831545]]]], 'bad_primes': [2, 3, 7], 'central_character': '4032.1567', 'coefficient_field': 'CDF', 'conductor': 4032, 'conductor_radical': 42, 'conjugate': '67118017334966870227087235516', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.768734305276283, 0], [5.0, 0]], [[1.0, 0], [-0.4809009198615832, -2.6016791318831545]], [[1.0, 0], [5.757390329120607, 0], [11.0, 0]], [[1.0, 0], [2.0, 0], [13.0, 0]], [[1.0, 0], [0, -6.719192168843773], [-17.0, 0]], [[1.0, 0], [0, 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'4.15379239440164883818555950801807', '4.89483835751750052586449250946706', '5.31837337394671025360524713341469', '6.89505442424972009885553110658784', '7.15532198465665684025236483483882', '7.977949338035910811098319792197339', '8.209043289921856757993058583868387'], 'prelabel': '2-4032-56.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.674123905501206, 'root_angle': 0.5251528144524793, 'root_number': '-0.0789376875004340773796250912070827495872650076454860813 + 0.9968795521486453950250235594565369354206898324357189932*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.26257640722623965', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.75161811497010203026987075404', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49479402271405981982089005889', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.14696368614023366014264416555', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.19568209498026, 'bad_primes': [2, 3, 7], 'central_character': '56.27', 'conductor': 4032, 'conductor_radical': 42, 'degree': 2, 'index': 39, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4032/2/p/j/1567/4'], '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': '2-4032-56.27-c1-0-39', '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': '2-4032-56.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.674123905501206, 'root_angle': 0.26257640722623965, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.75161811497010203026987075404', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '952789154584260173266526469478', 'Lhash_array': ['952789154584260173266526469478'], 'label': '2-4032-56.27-c1-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4032/2/p/j/1567/4'}