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lfunc_lfunctions • Show schema
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{'Lhash': '3944868482601645312521028707086', 'a10': [-19.35213725600914, -11.202445430555914], 'a2': [1.1755705045849463, -1.618033988749895], 'a3': [-4.1653149928521636, 1.3533928821918952], 'a4': [-1.2360679774997898, -3.804226065180614], 'a5': [-1.155966073772096, -11.120420065639964], 'a6': [-2.7067857643837905, 8.330629985704327], 'a7': [0.0, -31.20511383655954], 'a8': [-7.608452130361228, -2.4721359549995796], 'a9': [-6.325282152012249, 4.595586485070169], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.950095500287032, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.1755705045849463, 1.618033988749895]]], [5, [[1.0, 0], [1.155966073772096, 11.120420065639964]]]], 'bad_primes': [2, 5], 'central_character': '50.9', 'coefficient_field': 'CDF', 'conductor': 50, 'conductor_radical': 10, 'conjugate': '1135952392027247020808790547184', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.1755705045849463, 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'0.337030145362', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.11195252216297318117596230446', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.64457931331132645947077438665', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.16253298880257773947857267174', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.950095500287032, 'bad_primes': [2, 5], 'central_character': '25.9', 'conductor': 50, 'conductor_radical': 10, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/50/4/e/a/9/6'], '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': '2-50-25.9-c3-0-6', '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': '2-50-25.9-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7175842047151668, 'root_angle': 0.3370301453617275, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '3.11195252216297318117596230446', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3944868482601645312521028707086', 'Lhash_array': ['3944868482601645312521028707086'], 'label': '2-50-25.9-c3-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/50/4/e/a/9/6'}