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lfunc_lfunctions • Show schema
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{'Lhash': '1190702945040771204553073118637', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 3.7819388603335367], 'a6': [0, 0], 'a7': [-0.9535117355873467, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.542294840729653, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '864.161', 'coefficient_field': 'CDF', 'conductor': 864, 'conductor_radical': 6, 'conjugate': '1048989817576757962004629378021', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -3.7819388603335367], [-25.0, 0]], [[1.0, 0], [0.9535117355873467, 0], [49.0, 0]], [[1.0, 0], [0, 11.696938456699069], [-121.0, 0]], [[1.0, 0], [8.696938456699069, 0], [169.0, 0]], [[1.0, 0], [0, 4.7354505959208835], [-289.0, 0]], [[1.0, 0], [-29.2698910650651, 0], [361.0, 0]], [[1.0, 0], [0, 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'3.59774878977814720729834345240798', '4.80367892289515334690166928693785', '5.29815931199080916438167394875475', '6.62684707763213237899820448511291', '7.43695769368230045059136857493682', '8.252014905731431873679010012156819', '9.338472913140382267219944461382016', '9.732885595764637189194969842799359'], 'prelabel': '2-864-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8520402760828, 'root_angle': 0.0, 'root_number': '1', 'self_dual': False, 'sign_arg': 0, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.939299003074187441914200438649', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.27156273922677569525150618073', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.59774878977814720729834345241', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.542294840729653, 'bad_primes': [2, 3], 'central_character': '3.2', 'conductor': 864, 'conductor_radical': 6, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/864/3/e/f/161/5'], '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': '2-864-3.2-c2-0-14', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-864-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8520402760828, 'root_angle': 0.0, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.939299003074187441914200438649', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1190702945040771204553073118637', 'Lhash_array': ['1190702945040771204553073118637'], 'label': '2-864-3.2-c2-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/864/3/e/f/161/5'}