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lfunc_lfunctions • Show schema
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{'Lhash': '869867943412694818632822237243', 'a10': [0.0, 0.0], 'a2': [0.0, 1.0], 'a3': [0.0, 0.0], 'a4': [7.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 24.0], 'a8': [0.0, 15.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.199', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '2551707628207715927103078552094', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0], [-8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -24.0], [-343.0, 0]], [[1.0, 0], [52.0, 0], [1331.0, 0]], [[1.0, 0], [0, -22.0], [-2197.0, 0]], [[1.0, 0], [0, 14.0], [-4913.0, 0]], [[1.0, 0], [-20.0, 0], [6859.0, 0]], [[1.0, 0], [0, -168.0], [-12167.0, 0]], [[1.0, 0], [-230.0, 0], [24389.0, 0]], [[1.0, 0], [288.0, 0], 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'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.6475836176504333, 'root_number': '-0.4472135954999579 - 0.8944271909999159*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.323791808825', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68620481326327830775892603488', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.40800369120816277172154862329', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.64713644689738041200800205725', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.275429751291645, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/b/e/199/2'], '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': '2-15e2-5.4-c3-0-5', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-15e2-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.32379180882521663, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68620481326327830775892603488', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '869867943412694818632822237243', 'Lhash_array': ['869867943412694818632822237243'], 'label': '2-15e2-5.4-c3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/b/e/199/2'}