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lfunc_lfunctions • Show schema
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{'Lhash': '862973595121662014125446133172', 'a10': [18882514871.386772, 6607255014.70246], 'a2': [-1366.8895819878574, -478.29370751982555], 'a3': [0, 0], 'a4': [1639622.2586938792, 1307549.3718783937], 'a5': [-13814221.075506385, 0], 'a6': [0, 0], 'a7': [0, 1092598032.8569899], 'a8': [-1615789946.9631271, -2571496623.398069], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 201.22368788668473, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '10.5', 'prec': 14}, 'bad_lfactors': [[2, [[1.0, 0], [1366.8895819878574, 478.29370751982555]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '72.35', 'coefficient_field': 'CDF', 'conductor': 72, 'conductor_radical': 6, 'conjugate': '9469108715579409215758136050', 'degree': 2, 'euler_factors': [[[1.0, 0], [1366.8895819878574, 478.29370751982555]], [[1.0, 0], [0, 0]], [[1.0, 0], [13814221.075506385, 0], [476837158203125.0, 0]], [[1.0, 0], [0, -1092598032.8569899], [-558545864083284030, 0]], 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'3.32290696029129225600824502739', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 201.22368788668473, 'bad_primes': [2, 3], 'central_character': '24.11', 'conductor': 72, 'conductor_radical': 6, 'degree': 2, 'index': 49, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/72/22/f/a/35/9'], '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': '2-72-24.11-c21-0-49', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [21], 'order_of_vanishing': 0, 'prelabel': '2-72-24.11-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.18533354865809, 'root_angle': 0.3127571361959993, 'self_dual': False, 'spectral_label': 'c21-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68076613142950523384761081668', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '862973595121662014125446133172', 'Lhash_array': ['862973595121662014125446133172'], 'label': '2-72-24.11-c21-0-49', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/72/22/f/a/35/9'}