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lfunc_lfunctions • Show schema
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{'Lhash': '581584842191225790180081312413', 'a10': [0.0, 0.0], 'a2': [0.0, 2.070613028373415], 'a3': [-1.7843574765522912, -1.7843574765522912], 'a4': [-2.287438313269725, 0.0], 'a5': [0.0, 0.0], 'a6': [3.6947138382246845, -3.6947138382246845], 'a7': [0.2608949330902091, -0.2608949330902091], 'a8': [0.0, -0.5951735163099721], 'a9': [0.0, 3.3678632082561197], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.393642085904418, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [3.845583426242639, -1.4871072966695862]]]], 'bad_primes': [5, 17], 'central_character': '425.251', 'coefficient_field': 'CDF', 'conductor': 425, 'conductor_radical': 85, 'conjugate': '2183044743474059322054462033581', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.070613028373415], [-2.0, 0]], [[1.0, 0], [1.7843574765522912, 1.7843574765522912], [0, 3.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.2608949330902091, 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.45878954507378967587357711680', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.44791485572697754172012076659', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.79095893092929381277233356797', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.393642085904418, 'bad_primes': [5, 17], 'central_character': '17.13', 'conductor': 425, 'conductor_radical': 85, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/425/2/e/f/251/5'], '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': '2-425-17.13-c1-0-1', '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': '2-425-17.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8421840532108669, 'root_angle': -0.45322186001071413, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.45878954507378967587357711680', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '581584842191225790180081312413', 'Lhash_array': ['581584842191225790180081312413'], 'label': '2-425-17.13-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/425/2/e/f/251/5'}