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lfunc_lfunctions • Show schema
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{'Lhash': '791584444035361915128533437791', 'a10': [-2.2894838428169533, 0.0], 'a2': [-1.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [2.2894838428169533, 0.0], 'a6': [1.0, 0.0], 'a7': [-1.193778776572962, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.15181298389669, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [-1.0, 0]]], [103, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 13, 103], 'central_character': '8034.1', 'coefficient_field': 'CDF', 'conductor': 8034, 'conductor_radical': 8034, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.2894838428169533, 0], [5.0, 0]], [[1.0, 0], [1.193778776572962, 0], [7.0, 0]], [[1.0, 0], [-4.279050147687885, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.5957046761565064, 0], [17.0, 0]], [[1.0, 0], [1.3577007459125854, 0], 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'3.60779150013175953675925748948225', '4.15540767621612142369487368984345', '5.35174475465480757039955474947924', '5.92987964955260696976905348553970', '6.52049655421087663121516140308391', '6.89515879861318731309937648238863', '7.84509940883857872683386228668600'], 'prelabel': '2-8034-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.009482691403777, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62445002108060695948292282719', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.80055470522176618120902852368', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.19814247506004274765773294742', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.15181298389669, 'bad_primes': [2, 3, 13, 103], 'central_character': '1.1', 'conductor': 8034, 'conductor_radical': 8034, 'degree': 2, 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8034/2/a/z/1/12'], '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': '2-8034-1.1-c1-0-37', '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': '2-8034-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.009482691403777, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62445002108060695948292282719', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '791584444035361915128533437791', 'Lhash_array': ['791584444035361915128533437791'], 'label': '2-8034-1.1-c1-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8034/2/a/z/1/12'}