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lfunc_lfunctions • Show schema
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{'Lhash': '1940307482870992481979130837900', 'a10': [13.507810593582121, 0.0], 'a2': [2.7015621187164243, 0.0], 'a3': [3.0, 0.0], 'a4': [-0.7015621187164244, 0.0], 'a5': [5.0, 0.0], 'a6': [8.104686356149273, 0.0], 'a7': [-10.104686356149273, 0.0], 'a8': [-23.50781059358212, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 107.08846666041927, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-3.0, 0]]], [5, [[1.0, 0], [-5.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '1815.1', 'coefficient_field': 'CDF', 'conductor': 1815, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.7015621187164243, 0], [8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [-5.0, 0]], [[1.0, 0], [10.104686356149273, 0], [343.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [26.701562118716424, 0], [2197.0, 0]], [[1.0, 0], [-36.1937515251343, 0], [4913.0, 0]], [[1.0, 0], 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'4.41942383187225474871716831181072', '5.14888508436634696096398563784499', '5.93161425243261864579820129591845', '6.79645214995982563222528638763483', '7.62664622133695071014941374277995', '8.656113016066284948045230769136450'], 'prelabel': '2-1815-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.348355746707748, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.53063271734471398742545799061', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.94038978992505287738921907214', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24721496128905346592216008810', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 107.08846666041927, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 1815, 'conductor_radical': 165, 'degree': 2, 'index': 195, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1815/4/a/i/1/2'], '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': '2-1815-1.1-c3-0-195', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1815-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.348355746707748, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.53063271734471398742545799061', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1940307482870992481979130837900', 'Lhash_array': ['1940307482870992481979130837900'], 'label': '2-1815-1.1-c3-0-195', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1815/4/a/i/1/2'}