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lfunc_lfunctions • Show schema
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{'Lhash': '2076188319129527422034650971203', 'a10': [0.0, 0.0], 'a2': [-0.41421356237309503, 0.0], 'a3': [3.414213562373095, 0.0], 'a4': [-1.82842712474619, 0.0], 'a5': [0.0, 0.0], 'a6': [-1.4142135623730951, 0.0], 'a7': [0.585786437626905, 0.0], 'a8': [1.5857864376269049, 0.0], 'a9': [8.65685424949238, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.393642085904418, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 17], 'central_character': '425.1', 'coefficient_field': 'CDF', 'conductor': 425, 'conductor_radical': 85, 'conjugate': '2076188319129527422034650971203', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.41421356237309503, 0], [2.0, 0]], [[1.0, 0], [-3.414213562373095, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.585786437626905, 0], [7.0, 0]], [[1.0, 0], [2.585786437626905, 0], [11.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [13.0, 0]], 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'6.92871646654794529039133105579596', '8.025131764241853419421054187003934', '8.397931922459409570793110253071468', '9.169353683811902248069805882530935', '9.975485357724003750079855108178590', '10.73656684521069951269535552949188'], 'prelabel': '2-425-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8421840532108669, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.63782379683780994315413062874', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.09562835530497243281441072024', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.01125882588688955564358311101', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.393642085904418, 'bad_primes': [5, 17], 'central_character': '1.1', 'conductor': 425, 'conductor_radical': 85, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/425/2/a/f/1/1'], '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': '2-425-1.1-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': '2-425-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8421840532108669, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.63782379683780994315413062874', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2076188319129527422034650971203', 'Lhash_array': ['2076188319129527422034650971203'], 'label': '2-425-1.1-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/425/2/a/f/1/1'}