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lfunc_lfunctions • Show schema
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{'Lhash': '591394623006633359536464820456', 'a10': [21.618950038622252, 0], 'a2': [0, 3.445719568712378], 'a3': [0, 0], 'a4': [-7.872983346207417, 0], 'a5': [0, -6.274146693458568], 'a6': [0, 0], 'a7': [-8.872983346207416, 0], 'a8': [0, -13.345214505324044], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.673100788836337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '1089.485', 'coefficient_field': 'CDF', 'conductor': 1089, 'conductor_radical': 33, 'conjugate': '889872532919143644967171430760', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -3.445719568712378], [-4.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 6.274146693458568], [-25.0, 0]], [[1.0, 0], [8.872983346207416, 0], [49.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [24.745966692414832, 0], [169.0, 0]], [[1.0, 0], [0, -4.6803044566447545], [-289.0, 0]], [[1.0, 0], 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['0.46652809764785180634861064417643', '2.23345313990705584542537128421751', '2.95727290582062952216482524724376', '3.48121381102572871161516502510226', '4.69886566330150974334129433234715', '5.85673269928520070977571078377253', '7.05067719573992070744170274702161', '7.60981911397142270148640028134472', '9.285226739732629387058491722611499', '9.713605764365495964088721005913602'], 'prelabel': '2-33e2-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.447302156924686, 'root_angle': -0.6959132760153036, 'root_number': '-0.5773502691896257645091487805019574556476017512701268761 - 0.8164965809277260327324280249019637973219824935522233762*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3479566380076518', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.46652809764785180634861064418', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.23345313990705584542537128422', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.95727290582062952216482524724', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.673100788836337, 'bad_primes': [3, 11], 'central_character': '3.2', 'conductor': 1089, 'conductor_radical': 33, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1089/3/b/c/485/4'], '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': '2-33e2-3.2-c2-0-16', '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': '2-33e2-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.447302156924686, 'root_angle': -0.3479566380076518, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.46652809764785180634861064418', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '591394623006633359536464820456', 'Lhash_array': ['591394623006633359536464820456'], 'label': '2-33e2-3.2-c2-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1089/3/b/c/485/4'}