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lfunc_lfunctions • Show schema
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{'Lhash': '1109547081359814519117639491395', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -0.6656468759659453], 'a6': [0, 0], 'a7': [0, 1.0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.19568209498026, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3, 7], 'central_character': '4032.575', 'coefficient_field': 'CDF', 'conductor': 4032, 'conductor_radical': 42, 'conjugate': '764211808285536080451103775292', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0.6656468759659453], [-5.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [-2.07986043833904, 0], [11.0, 0]], [[1.0, 0], [5.556914236516778, 0], [13.0, 0]], [[1.0, 0], [0, 2.162780248780245], [-17.0, 0]], [[1.0, 0], [0, -4.498281076259099], [-19.0, 0]], [[1.0, 0], [4.28166966707282, 0], [23.0, 0]], 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'3.99428340275457118491062983248273', '4.71472347883789054495907779576262', '5.46924620279390791921142056301158', '6.56150049596875855719387815083440', '6.96575300745726664277794480518210', '7.67811400812115790353488572052399', '8.547200039390650689585584996179101'], 'prelabel': '2-4032-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.674123905501206, 'root_angle': 0.19591327601530362, 'root_number': '0.8164965809277260327324280249019637973219824935522233761 + 0.5773502691896257645091487805019574556476017512701268760*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.09795663800765182', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.875278314986834915823927579903', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.17784153476863363437713306591', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.97189243091398691759292514096', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.19568209498026, 'bad_primes': [2, 3, 7], 'central_character': '12.11', 'conductor': 4032, 'conductor_radical': 42, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4032/2/h/h/575/6'], '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': '2-4032-12.11-c1-0-22', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-4032-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.674123905501206, 'root_angle': 0.09795663800765181, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.875278314986834915823927579903', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1109547081359814519117639491395', 'Lhash_array': ['1109547081359814519117639491395'], 'label': '2-4032-12.11-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4032/2/h/h/575/6'}