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lfunc_lfunctions • Show schema
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{'Lhash': '1341026051851109219410743596610', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0.17364817766693036, 0.3007674663608706], 'a6': [0, 0], 'a7': [0.6736481776669303, -1.1667928701453092], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.522918152936914, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1944.649', 'coefficient_field': 'CDF', 'conductor': 1944, 'conductor_radical': 6, 'conjugate': '1094020197081040595762824572082', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.17364817766693036, -0.3007674663608706], [-2.5, 4.330127018922194]], [[1.0, 0], [-0.6736481776669303, 1.1667928701453092], [-3.5, -6.06217782649107]], [[1.0, 0], [-0.09239626545204768, 0.16003502619256754], [-5.5, -9.526279441628825]], [[1.0, 0], [-0.9187480877851173, 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'root_analytic_conductor': 3.9399134702347096, 'root_angle': 0.1111111111111111, 'root_number': '0.93969262078590838405410927732473146993620813426446463309 + 0.3420201433256687330440996146822595807630833675141606285*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.05555555555555555', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05788302518822553290197873251', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.29720325165664490900739011859', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.34098167306856885368379635096', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.522918152936914, 'bad_primes': [2, 3], 'central_character': '9.7', 'conductor': 1944, 'conductor_radical': 6, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1944/2/i/o/649/2'], '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': '2-1944-9.7-c1-0-20', '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': '2-1944-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9399134702347096, 'root_angle': 0.05555555555555555, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05788302518822553290197873251', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1341026051851109219410743596610', 'Lhash_array': ['1341026051851109219410743596610'], 'label': '2-1944-9.7-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1944/2/i/o/649/2'}