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lfunc_lfunctions • Show schema
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{'Lhash': '4546962526567598540271758353941', 'a10': [2.0, 0.3360827212213939], 'a2': [0.0, -0.9069676505260347], 'a3': [0.0, -3.217890514265296], 'a4': [1.1774096808992847, 0.0], 'a5': [-0.3705564592369621, 2.205150314721825], 'a6': [-2.9185225993732087, 0.0], 'a7': [0.0, 2.5963653283915815], 'a8': [0.0, -2.881807793043902], 'a9': [-7.354819361798569, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.758578819202164, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0.3705564592369621, -2.205150314721825]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 19], 'central_character': '95.39', 'coefficient_field': 'CDF', 'conductor': 95, 'conductor_radical': 95, 'conjugate': '2459241620020596543703693530545', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0.9069676505260347], [-2.0, 0]], [[1.0, 0], [0, 3.217890514265296], [-3.0, 0]], [[1.0, 0], [0.3705564592369621, -2.205150314721825]], [[1.0, 0], [0, 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'4.83373972503331346542571536512530', '5.87699445232068947900000267677400', '7.77735111826024365539520968831366', '8.778170423991545566308717387674296', '10.06730519505426476062548326502123', '10.81081115481720680696671099631755', '11.90795840004636965826270360202096', '13.54030201642064528606940691130636', '14.79744443724202984233047766877909'], 'prelabel': '2-95-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8709643042066443, 'root_angle': 0.5529941137908199, 'root_number': '-0.16571788647109556 + 0.9861732008646114*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.276497056895', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.58692097471413472529163800639', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.83373972503331346542571536513', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.87699445232068947900000267677', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.758578819202164, 'bad_primes': [5, 19], 'central_character': '5.4', 'conductor': 95, 'conductor_radical': 95, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/95/2/b/b/39/3'], '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': '2-95-5.4-c1-0-6', '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': '2-95-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8709643042066443, 'root_angle': 0.27649705689540993, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.58692097471413472529163800639', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4546962526567598540271758353941', 'Lhash_array': ['4546962526567598540271758353941'], 'label': '2-95-5.4-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/95/2/b/b/39/3'}