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lfunc_lfunctions • Show schema
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{'Lhash': '331285837081071036163817376481', 'a10': [9.409074749883755, 0.0], 'a2': [-2.2710198793226337, 0.0], 'a3': [-0.7852309733282328, 0.0], 'a4': [3.1575312922785894, 0.0], 'a5': [-4.14310541072417, 0.0], 'a6': [1.7832751502882773, 0.0], 'a7': [0.0, 0.0], 'a8': [-2.628776575702694, 0.0], 'a9': [-2.383412318525996, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 55.951176696311194, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [7, 11, 13], 'central_character': '7007.1', 'coefficient_field': 'CDF', 'conductor': 7007, 'conductor_radical': 1001, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.2710198793226337, 0], [2.0, 0]], [[1.0, 0], [0.7852309733282328, 0], [3.0, 0]], [[1.0, 0], [4.14310541072417, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [6.368894826633459, 0], [17.0, 0]], 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'2.59593931500891603842543126984073', '3.43318682984238043942045003288097', '4.36487623292247811127852186602931', '5.01884180519815612788933624024186', '6.31943725297044093332079680116382', '6.77306473358682951415769523948787', '7.45434229862280458592647244142045', '8.125532314976648393406761481619613'], 'prelabel': '2-7007-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.480051918022441, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.26133844532667433691809998730', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.29412400289930194479658337532', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.59593931500891603842543126984', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 55.951176696311194, 'bad_primes': [7, 11, 13], 'central_character': '1.1', 'conductor': 7007, 'conductor_radical': 1001, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7007/2/a/bi/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': '2-7007-1.1-c1-0-18', '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': '2-7007-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.480051918022441, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.26133844532667433691809998730', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '331285837081071036163817376481', 'Lhash_array': ['331285837081071036163817376481'], 'label': '2-7007-1.1-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7007/2/a/bi/1/2'}