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lfunc_lfunctions • Show schema
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{'Lhash': '1175800677826790762755516810499', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-200.2690669750293, -137.62739848210177], 'a4': [0, 0], 'a5': [0, 3630.4734623746162], 'a6': [0, 0], 'a7': [23226.529616651584, 0], 'a8': [0, 0], 'a9': [21166.398374097538, 55125.021368422174], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 121.98859251335509, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [200.2690669750293, 137.62739848210177]]]], 'bad_primes': [2, 3], 'central_character': '192.65', 'coefficient_field': 'CDF', 'conductor': 192, 'conductor_radical': 6, 'conjugate': '736800090947295201371905320342', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [200.2690669750293, 137.62739848210177]], [[1.0, 0], [0, -3630.4734623746162], [-9765625.0, 0]], [[1.0, 0], [-23226.529616651584, 0], [282475249.0, 0]], [[1.0, 0], [0, -62442.66823691063], [-25937424601.0, 0]], [[1.0, 0], 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0.5663678949880731548340188687487964292109602638384880847*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.09582592887113932', 'prec': 64}, 'spectral_label': 'c10-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.927543187069921424963790514847', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.57833705181264508389992955616', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.72754170224257722961055606495', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 121.98859251335509, 'bad_primes': [2, 3], 'central_character': '3.2', 'conductor': 192, 'conductor_radical': 6, 'degree': 2, 'index': 50, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/11/e/h/65/1'], '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': '2-192-3.2-c10-0-50', 'motivic_weight': 10, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [10], 'order_of_vanishing': 0, 'prelabel': '2-192-3.2-c10-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.044844612458569, 'root_angle': 0.09582592887113932, 'self_dual': False, 'spectral_label': 'c10-0', 'z1': {'__RealLiteral__': 0, 'data': '0.927543187069921424963790514847', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1175800677826790762755516810499', 'Lhash_array': ['1175800677826790762755516810499'], 'label': '2-192-3.2-c10-0-50', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/11/e/h/65/1'}