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lfunc_lfunctions • Show schema
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{'Lhash': '159793421715353677405572487805,2111727050304231285969338944123', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 14, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5412.496546560998, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '2700.1', 'coefficient_field': '1.1.1.1', 'conductor': 7290000, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1], [1], [1, -14, 147, -686, 2401], [1, 0, -62, 0, 14641], [1, 34, 627, 5746, 28561], [1, 0, 142, 0, 83521], [1, -22, 843, -7942, 130321], [1, 0, 562, 0, 279841], [1, 0, -62, 0, 707281], [1, 116, 5286, 111476, 923521], [1, -14, 2787, -19166, 1874161], [1, 0, 1138, 0, 2825761], [1, 52, 4374, 96148, 3418801], [1, 0, -4418, 0, 4879681], [1, 0, -3998, 0, 7890481], [1, 0, -6242, 0, 12117361], [1, 2, 7443, 7442, 13845841], [1, 226, 21747, 1014514, 20151121], [1, 0, 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'spectral_label': 'c2e2-0', 'trace_hash': 271843899896171179, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.12605478330273678697946599349', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.27347129428514195813543059172', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.66585891248269302550360882605', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5412.496546560998, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 7290000, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, -34, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -116, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 0, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -226, 0, 0, 0, 0, 0, 86, 0, 0, 0, 0, 0, -98, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -476, 0, 0, 0, 0, 0, -226, 0, 0, 0], 'euler11': [1, 0, -62, 0, 14641], 'euler13': [1, 34, 627, 5746, 28561], 'euler17': [1, 0, 142, 0, 83521], 'euler19': [1, -22, 843, -7942, 130321], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 562, 0, 279841], 'euler29': [1, 0, -62, 0, 707281], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 116, 5286, 111476, 923521], 'euler37': [1, -14, 2787, -19166, 1874161], 'euler41': [1, 0, 1138, 0, 2825761], 'euler43': [1, 52, 4374, 96148, 3418801], 'euler47': [1, 0, -4418, 0, 4879681], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -3998, 0, 7890481], 'euler59': [1, 0, -6242, 0, 12117361], 'euler61': [1, 2, 7443, 7442, 13845841], 'euler67': [1, 226, 21747, 1014514, 20151121], 'euler7': [1, -14, 147, -686, 2401], 'euler71': [1, 0, -5582, 0, 25411681], 'euler73': [1, -86, 12507, -458294, 28398241], 'euler79': [1, 98, 14883, 611618, 38950081], 'euler83': [1, 0, -12158, 0, 47458321], 'euler89': [1, 0, -15122, 0, 62742241], 'euler97': [1, 226, 31587, 2126434, 88529281], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -14, 147, -686, 2401], [1, 0, -62, 0, 14641], [1, 34, 627, 5746, 28561], [1, 0, 142, 0, 83521], [1, -22, 843, -7942, 130321], [1, 0, 562, 0, 279841], [1, 0, -62, 0, 707281], [1, 116, 5286, 111476, 923521], [1, -14, 2787, -19166, 1874161], [1, 0, 1138, 0, 2825761], [1, 52, 4374, 96148, 3418801], [1, 0, -4418, 0, 4879681], [1, 0, -3998, 0, 7890481], [1, 0, -6242, 0, 12117361], [1, 2, 7443, 7442, 13845841], [1, 226, 21747, 1014514, 20151121], [1, 0, -5582, 0, 25411681], [1, -86, 12507, -458294, 28398241], [1, 98, 14883, 611618, 38950081], [1, 0, -12158, 0, 47458321], [1, 0, -15122, 0, 62742241], [1, 226, 31587, 2126434, 88529281]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2700/3/g/l'], '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': '4-2700e2-1.1-c2e2-0-3', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'prelabel': '4-2700e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.577276454520991, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 271843899896171179, 'z1': {'__RealLiteral__': 0, 'data': '0.12605478330273678697946599349', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '159793421715353677405572487805,2111727050304231285969338944123', 'Lhash_array': ['159793421715353677405572487805', '2111727050304231285969338944123'], 'factors': ['2-2700-3.2-c2-0-4', '2-2700-3.2-c2-0-50'], 'label': '4-2700e2-1.1-c2e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2700/3/g/l'}