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lfunc_lfunctions • Show schema
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{'Lhash': '6098684805566804101904576847973', 'a10': [-79.2007738856876, -61.05110495239366], 'a2': [1.355626179974266, -3.763280172956616], 'a3': [-13.996237488841103, 0.0], 'a4': [-12.324555320336758, -10.203202250076144], 'a5': [7.649110640673517, -23.801073639790605], 'a6': [-18.973665961010276, 52.67176303774782], 'a7': [35.686256368429355, 0.0], 'a8': [-55.10499857716752, 32.549026587754746], 'a9': [114.8946638440411, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.0673992616768873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.355626179974266, 3.763280172956616]]], [5, [[1.0, 0], [-7.649110640673517, 23.801073639790605]]]], 'bad_primes': [2, 5], 'central_character': '20.19', 'coefficient_field': 'CDF', 'conductor': 20, 'conductor_radical': 10, 'conjugate': '1149019787343312558521989433394', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.355626179974266, 3.763280172956616]], [[1.0, 0], 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'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.81101401637705946130155288369', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.21049226341032687636370428370', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.46180922645521559262092255964', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.0673992616768873, 'bad_primes': [2, 5], 'central_character': '20.19', 'conductor': 20, 'conductor_radical': 10, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/20/5/d/c/19/5'], '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': '2-20-20.19-c4-0-9', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-20-20.19-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4378453538808988, 'root_angle': 0.4095464812183277, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '4.81101401637705946130155288369', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '6098684805566804101904576847973', 'Lhash_array': ['6098684805566804101904576847973'], 'label': '2-20-20.19-c4-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/20/5/d/c/19/5'}