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lfunc_lfunctions • Show schema
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{'Lhash': '487530153464115122301097985517', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 3.0], 'a4': [0.0, 0.0], 'a5': [0.0, 10.392304845413264], 'a6': [0.0, 0.0], 'a7': [-3.4641016151377544, 0.0], 'a8': [0.0, 0.0], 'a9': [-9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.328366721102203, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, -3.0]]]], 'bad_primes': [2, 3], 'central_character': '192.97', 'coefficient_field': 'CDF', 'conductor': 192, 'conductor_radical': 6, 'conjugate': '2941840213966578917764416375898', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -3.0]], [[1.0, 0], [0, -10.392304845413264], [-125.0, 0]], [[1.0, 0], [3.4641016151377544, 0], [343.0, 0]], [[1.0, 0], [0, 0], [-1331.0, 0]], [[1.0, 0], [0, -55.42562584220407], [-2197.0, 0]], [[1.0, 0], [90.0, 0], [4913.0, 0]], [[1.0, 0], [0, 116.0], [-6859.0, 0]], [[1.0, 0], [103.92304845413264, 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'8.444558517412407775253868476438320', '9.549438467199066509943249325938740', '10.68040472437362072982510926193502', '11.86666870918728871999911308415516'], 'prelabel': '2-192-8.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.365763913452963, 'root_angle': -0.9166666666666667, 'root_number': '-0.9659258262890683 - 0.2588190451025206*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.458333333333', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.38459347818424065981239101587', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.03181003938150826439498077059', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83949570730201878639250192108', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.328366721102203, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 192, 'conductor_radical': 6, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/4/d/a/97/4'], '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': '2-192-8.5-c3-0-2', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-192-8.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.365763913452963, 'root_angle': -0.45833333333333337, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.38459347818424065981239101587', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '487530153464115122301097985517', 'Lhash_array': ['487530153464115122301097985517'], 'label': '2-192-8.5-c3-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/4/d/a/97/4'}