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lfunc_lfunctions • Show schema
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{'Lhash': '779058579902059968188249842916', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-21.417864429562457, 7.79546513390961], 'a4': [0.0, 0.0], 'a5': [5.95220808325002, -33.756649489117414], 'a6': [0.0, 0.0], 'a7': [-60.035346669552695, -103.98427068167625], 'a8': [0.0, 0.0], 'a9': [211.8068403912047, -177.72704165308488], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.189170305786531, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-474.4005597873504, -1500.3476626680392]]]], 'bad_primes': [2, 19], 'central_character': '76.73', 'coefficient_field': 'CDF', 'conductor': 76, 'conductor_radical': 38, 'conjugate': '1290483831585356022147361453760', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [21.417864429562457, -7.79546513390961], [186.14879967791165, -156.19738915382905]], [[1.0, 0], [-5.95220808325002, 33.756649489117414], [-2936.5394399559636, -1068.8129478927149]], 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103}, 'z2': {'__RealLiteral__': 0, 'data': '2.84689438614839780784489630257', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.18716560422136339081927273354', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.189170305786531, 'bad_primes': [2, 19], 'central_character': '19.16', 'conductor': 76, 'conductor_radical': 38, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/76/6/i/a/73/1'], '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': '2-76-19.16-c5-0-1', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-76-19.16-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4912992289098526, 'root_angle': -0.134485631725282, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.61456885656173498113490564961', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '779058579902059968188249842916', 'Lhash_array': ['779058579902059968188249842916'], 'label': '2-76-19.16-c5-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/76/6/i/a/73/1'}