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lfunc_lfunctions • Show schema
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{'Lhash': '2011897950315261481389662128349', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.5256871208655185, 2.6425676097925566], 'a4': [0.0, 0.0], 'a5': [-0.6297552606843122, 1.090768107839012], 'a6': [0.0, 0.0], 'a7': [1.5256871208655185, -2.6425676097925566], 'a8': [0.0, 0.0], 'a9': [-3.1554423815498307, -5.465386525200445], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.727143799659801, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [1.3702447393156878, 5.926417919314979]]]], 'bad_primes': [2, 37], 'central_character': '592.433', 'coefficient_field': 'CDF', 'conductor': 592, 'conductor_radical': 74, 'conjugate': '177324269530495373474086577357', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.5256871208655185, -2.6425676097925566], [-1.5, -2.598076211353316]], [[1.0, 0], [0.6297552606843122, -1.090768107839012], [-2.5, -4.330127018922194]], [[1.0, 0], 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'root_analytic_conductor': 2.1741995767775784, 'root_angle': 0.4744986764920295, 'root_number': '0.08002909696199592 + 0.9967925278810267*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.237249338246', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.58710763829799540582402163984', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.64697035514629600978281620335', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.75616101250111957534249869366', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.727143799659801, 'bad_primes': [2, 37], 'central_character': '37.26', 'conductor': 592, 'conductor_radical': 74, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/592/2/i/e/433/1'], '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': '2-592-37.26-c1-0-11', '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': '2-592-37.26-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1741995767775784, 'root_angle': 0.23724933824601474, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.58710763829799540582402163984', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2011897950315261481389662128349', 'Lhash_array': ['2011897950315261481389662128349'], 'label': '2-592-37.26-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/592/2/i/e/433/1'}