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lfunc_lfunctions • Show schema
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{'Lhash': '1163728945502579081948892103693', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.5, -0.8660254037844386], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [2.612499217514678, -0.418148105920851], 'a8': [0, 0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.768584424468887, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.5, 0.8660254037844386]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.612499217514678, 0.418148105920851]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '2100.1801', 'coefficient_field': 'CDF', 'conductor': 2100, 'conductor_radical': 210, 'conjugate': '1244589731930482104674363378196', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.612499217514678, 0.418148105920851]], [[1.0, 0], [-0.29238749828270305, -0.5064300025235995], [-5.5, 9.526279441628825]], 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'9.347874102485816066219410874003896'], 'prelabel': '2-2100-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.0949462053205155, 'root_angle': 0.0959745654827759, 'root_number': '0.95488827677394375019276207882371799044106310284212862918 + 0.2969652822800810106776778046785645125269815097225202811*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.04798728274138795', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.918020269381058049675684272833', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.28028614132310426734802559159', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.39189986697798024997674546928', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.768584424468887, 'bad_primes': [2, 3, 5, 7], 'central_character': '7.2', 'conductor': 2100, 'conductor_radical': 210, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2100/2/q/l/1801/4'], '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': '2-2100-7.2-c1-0-13', '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': '2-2100-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.0949462053205155, 'root_angle': 0.04798728274138795, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.918020269381058049675684272833', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1163728945502579081948892103693', 'Lhash_array': ['1163728945502579081948892103693'], 'label': '2-2100-7.2-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2100/2/q/l/1801/4'}