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lfunc_lfunctions • Show schema
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{'Lhash': '2670453724364743894895060137517', 'a10': [-6.644589580730847e-61, 0.13052518180078873], 'a2': [0.040334499370323317, 0.12413682469224971], 'a3': [-1.7281864274579546, -0.11563594575265898], 'a4': [1.604250909344675, -1.1655565112301793], 'a5': [0.9510565162951535, 0.30901699437494745], 'a6': [-0.05535085524408385, -0.2191956935620208], 'a7': [-1.5033920455970706, -2.0692416309399824], 'a8': [0.4205893221377297, 0.30557602935800726], 'a9': [2.9732566560997764, 0.3996809439520191], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3175316333511269, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.7281864274579546, 0.11563594575265898]]], [5, [[1.0, 0], [-0.9510565162951535, -0.30901699437494745]]], [11, [[1.0, 0], [-1.1270747457200148, 3.119247107486062]]]], 'bad_primes': [3, 5, 11], 'central_character': '165.116', 'coefficient_field': 'CDF', 'conductor': 165, 'conductor_radical': 165, 'conjugate': 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'data': '0.112318412195', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.10661654235319421791046862727', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.96981646553223542512315608591', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.58394370784669155972409417757', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3175316333511269, 'bad_primes': [3, 5, 11], 'central_character': '33.17', 'conductor': 165, 'conductor_radical': 165, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/165/2/p/b/116/7'], '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': '2-165-33.17-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': '2-165-33.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1478378079463696, 'root_angle': 0.11231841219454852, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.10661654235319421791046862727', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2670453724364743894895060137517', 'Lhash_array': ['2670453724364743894895060137517'], 'label': '2-165-33.17-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/165/2/p/b/116/7'}