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lfunc_lfunctions • Show schema
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{'Lhash': '3521644164556418863281153830784', 'a10': [1.3499317546350558, 2.7282835425402316], 'a2': [1.3561314327060396, 0.11864612661294795], 'a3': [0.8015460233949577, -1.5354230597394745], 'a4': [-0.1445999466113361, -0.025496871996582127], 'a5': [1.1625408872302507, 1.910104365085296], 'a6': [1.2691737558367224, -1.9871351428365616], 'a7': [0.49526303477594397, 0.3467869103467336], 'a8': [-2.8229235583818735, -0.7564000877632143], 'a9': [-1.7150479447594595, -2.461424495526189], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0779804272872857, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.8015460233949577, 1.5354230597394745]]], [5, [[1.0, 0], [-1.1625408872302507, -1.910104365085296]]]], 'bad_primes': [3, 5], 'central_character': '135.113', 'coefficient_field': 'CDF', 'conductor': 135, 'conductor_radical': 15, 'conjugate': '3015575867145279897124268426692', 'degree': 2, 'euler_factors': [[[1.0, 0], 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50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.77808740351827044287333493702', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.42221565178092042457384365876', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.90616321863577152001769558714', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0779804272872857, 'bad_primes': [3, 5], 'central_character': '135.113', 'conductor': 135, 'conductor_radical': 15, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/135/2/q/a/113/12'], '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': '2-135-135.113-c1-0-11', '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': '2-135-135.113-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0382583624933082, 'root_angle': 0.05488015164577323, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.77808740351827044287333493702', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3521644164556418863281153830784', 'Lhash_array': ['3521644164556418863281153830784'], 'factors': ['2-135-135.113-c1-0-11'], 'label': '2-135-135.113-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/135/2/q/a/113/12'}