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lfunc_lfunctions • Show schema
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{'Lhash': '3475624941386635534558315972216', 'a10': [0.0, 0.0], 'a2': [0.0, 0.6180339887498949], 'a3': [0.0, -3.23606797749979], 'a4': [1.618033988749895, 0.0], 'a5': [0.0, 0.0], 'a6': [2.0, 0.0], 'a7': [0.0, -1.0], 'a8': [0.0, 2.23606797749979], 'a9': [-7.47213595499958, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3973820353724073, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [5, 7], 'central_character': '175.99', 'coefficient_field': 'CDF', 'conductor': 175, 'conductor_radical': 35, 'conjugate': '1903135665556813113054430709495', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -0.6180339887498949], [-2.0, 0]], [[1.0, 0], [0, 3.23606797749979], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0.2360679774997897, 0], [11.0, 0]], [[1.0, 0], [0, -1.2360679774997898], [-13.0, 0]], [[1.0, 0], [0, 2.4721359549995796], [-17.0, 0]], [[1.0, 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'10.09210118858198878118867805189141', '10.79593599637896004221013706162083', '11.56113045395214947258880427252468', '12.55833065602628834637162321434422'], 'prelabel': '2-175-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.182109146979418, 'root_angle': 0.35241638234956674, 'root_number': '0.44721359549995804 + 0.8944271909999159*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.176208191175', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.74178463747098740592672550607', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.81330912581320927380422688031', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.15070445306339661512659339848', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3973820353724073, 'bad_primes': [5, 7], 'central_character': '5.4', 'conductor': 175, 'conductor_radical': 35, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/175/2/b/c/99/3'], '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': '2-175-5.4-c1-0-7', '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': '2-175-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.182109146979418, 'root_angle': 0.17620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.74178463747098740592672550607', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3475624941386635534558315972216', 'Lhash_array': ['3475624941386635534558315972216'], 'label': '2-175-5.4-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/175/2/b/c/99/3'}