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lfunc_lfunctions • Show schema
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{'Lhash': '4550156540727536811956799645442', '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': [-6.076624599100714e-61, -0.7320508075688773], 'a7': [-2.0, 3.4641016151377544], '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], [0.5, 6.06217782649107]]]], 'bad_primes': [2, 37], 'central_character': '74.11', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '3186580474100743147525674365857', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [-0.36602540378443865, 0.6339745962155614], [-1.5, -2.598076211353316]], [[1.0, 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'root_analytic_conductor': 0.7686956321961738, 'root_angle': 0.2134907334186144, 'root_number': '0.7833862120526783 + 0.6215352305105127*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.106745366709', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.58944060761563235987323413755', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.35454702863015530219870428384', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.78100534759549792262131656320', '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': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/2/e/a/11/2'], '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-c1-0-3', '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': 0.1067453667093072, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.58944060761563235987323413755', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4550156540727536811956799645442', 'Lhash_array': ['4550156540727536811956799645442'], 'label': '2-74-37.11-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/2/e/a/11/2'}