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lfunc_lfunctions • Show schema
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{'Lhash': '1877263515119465207268015417573', 'a10': [-6.291502622129181, 10.897202197480558], 'a2': [-1.224744871391589, 0.7071067811865476], 'a3': [0, 0], 'a4': [1.0, -1.7320508075688772], 'a5': [7.705485569799449, -4.448764167960489], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 2.8284271247461903], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.03275931657819, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.224744871391589, -0.7071067811865476]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '882.557', 'coefficient_field': 'CDF', 'conductor': 882, 'conductor_radical': 42, 'conjugate': '787076179696285830917274484321', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.224744871391589, -0.7071067811865476]], [[1.0, 0], [0, 0]], [[1.0, 0], [-7.705485569799449, 4.448764167960489], [12.5, -21.650635094610966]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'9.703387230799430714878179436073888', '10.09833356062295349686689066404399'], 'prelabel': '2-882-21.11-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.902321829151794, 'root_angle': 0.43040748454347083, 'root_number': '0.2168937427126198451204379472713968874232571735022005397 + 0.9761952183718745637671305469550791571164894409176918445*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.21520374227173542', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48089979587551990523158002969', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48487901465152878734149588800', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.25206946935532415342913591027', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.03275931657819, 'bad_primes': [2, 3, 7], 'central_character': '21.11', 'conductor': 882, 'conductor_radical': 42, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/882/3/s/e/557/2'], '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': '2-882-21.11-c2-0-20', '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': '2-882-21.11-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.902321829151794, 'root_angle': 0.21520374227173542, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48089979587551990523158002969', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1877263515119465207268015417573', 'Lhash_array': ['1877263515119465207268015417573'], 'label': '2-882-21.11-c2-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/882/3/s/e/557/2'}