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lfunc_lfunctions • Show schema
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{'Lhash': '2888883909800366675803761789330', 'a10': [-1.7320508075688772, 6.873352803342883e-62], 'a2': [-0.8660254037844386, 0.5], 'a3': [0.36602540378443865, -0.6339745962155614], 'a4': [0.5, -0.8660254037844386], 'a5': [1.5, 0.8660254037844386], 'a6': [3.7988429192648594e-61, 0.7320508075688773], 'a7': [1.0, -1.7320508075688772], 'a8': [0.0, 1.0], 'a9': [1.2320508075688772, 2.133974596215561], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, -0.5]]], [37, [[1.0, 0], [-4.696152422706632, -3.866025403784439]]]], 'bad_primes': [2, 37], 'central_character': '74.11', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '2776377093941725433236058857069', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [-0.36602540378443865, 0.6339745962155614], [-1.5, 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'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': -0.04107967679264207, 'root_number': '0.9916838766051965 - 0.12869766463028515*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0205398383963', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.27892757616353307373626938367', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.46680475983487499123560289942', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.20786681146086478404619554734', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'bad_primes': [2, 37], 'central_character': '37.11', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/2/e/b/11/1'], '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': '2-74-37.11-c1-0-2', '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': '2-74-37.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': -0.020539838396321036, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.27892757616353307373626938367', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2888883909800366675803761789330', 'Lhash_array': ['2888883909800366675803761789330'], 'label': '2-74-37.11-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/2/e/b/11/1'}