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lfunc_lfunctions • Show schema
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{'Lhash': '836021561500139008328308176774', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 4.878315177510849], 'a6': [0, 0], 'a7': [-11.797958971132712, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31.389726454306206, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1152.1025', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '1030756963093128598948237664999', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -4.878315177510849], [-25.0, 0]], [[1.0, 0], [11.797958971132712, 0], [49.0, 0]], [[1.0, 0], [0, 9.756630355021699], [-121.0, 0]], [[1.0, 0], [-22.69693845669907, 0], [169.0, 0]], [[1.0, 0], [0, 22.198823253199624], [-289.0, 0]], [[1.0, 0], [17.79795897113271, 0], [361.0, 0]], [[1.0, 0], [0, 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'4.11851923872372311323664836201975', '5.29525766982348591059551325014375', '6.44756765501538743747378083602033', '6.60254571919395091490225932391404', '8.192034542764595410489857805896563', '8.700185395165093062142203689524595', '9.445018437573873286520840744080494'], 'prelabel': '2-1152-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.602653519030621, 'root_angle': -0.19591327601530362, 'root_number': '0.8164965809277260327324280249019637973219824935522233762 - 0.5773502691896257645091487805019574556476017512701268760*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.09795663800765182', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.65950472578928345040594991349', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.00529509394838221187036970604', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.49606165359999204617861739657', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 31.389726454306206, 'bad_primes': [2, 3], 'central_character': '3.2', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/3/e/d/1025/4'], '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': '2-1152-3.2-c2-0-11', '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': '2-1152-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.602653519030621, 'root_angle': -0.09795663800765181, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.65950472578928345040594991349', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '836021561500139008328308176774', 'Lhash_array': ['836021561500139008328308176774'], 'label': '2-1152-3.2-c2-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/3/e/d/1025/4'}