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lfunc_lfunctions • Show schema
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{'Lhash': '2261447573239440953572780461722', 'a10': [-2.366025403784439, -0.6339745962155614], 'a2': [-1.3660254037844386, 0.36602540378443865], 'a3': [-0.8660254037844386, -1.5], 'a4': [1.7320508075688772, -1.0], 'a5': [1.5, 0.8660254037844386], 'a6': [1.7320508075688772, 1.7320508075688772], 'a7': [0.0, 0.0], 'a8': [-2.0, 2.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5650678796170963, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3660254037844386, -0.36602540378443865]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '196.19', 'coefficient_field': 'CDF', 'conductor': 196, 'conductor_radical': 14, 'conjugate': '1352278398907458244262822025767', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3660254037844386, -0.36602540378443865]], [[1.0, 0], [0.8660254037844386, 1.5], [-1.5, 2.598076211353316]], [[1.0, 0], [-1.5, -0.8660254037844386], [2.5, 4.330127018922194]], 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.78396757973552578333510768553', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.79688584054174697644332884819', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.26238408978096231976593731906', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5650678796170963, 'bad_primes': [2, 7], 'central_character': '28.19', 'conductor': 196, 'conductor_radical': 14, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/196/2/f/a/19/1'], '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': '2-14e2-28.19-c1-0-6', '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': '2-14e2-28.19-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.251026730176896, 'root_angle': 0.15658019013969363, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.78396757973552578333510768553', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2261447573239440953572780461722', 'Lhash_array': ['2261447573239440953572780461722'], 'label': '2-14e2-28.19-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/196/2/f/a/19/1'}