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lfunc_lfunctions • Show schema
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{'Lhash': '3376152328375953057504042135470', 'a10': [0.0, 0.0], 'a2': [1.4142135623730951, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.0, 0.0], 'a8': [-2.8284271247461903, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.389902136436429, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '675.1', 'coefficient_field': 'CDF', 'conductor': 675, 'conductor_radical': 15, 'conjugate': '3376152328375953057504042135470', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4142135623730951, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.0, 0], [7.0, 0]], [[1.0, 0], [4.242640687119285, 0], [11.0, 0]], [[1.0, 0], [3.0, 0], [13.0, 0]], [[1.0, 0], [2.8284271247461903, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0], [19.0, 0]], [[1.0, 0], [-7.0710678118654755, 0], [23.0, 0]], 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2.321616276742655, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.66331458192668103061953617832', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.31542830773422409085022841573', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.68147121582242178577071732276', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.389902136436429, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 675, 'conductor_radical': 15, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/675/2/a/l/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': '2-675-1.1-c1-0-24', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-675-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.321616276742655, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.66331458192668103061953617832', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3376152328375953057504042135470', 'Lhash_array': ['3376152328375953057504042135470'], 'label': '2-675-1.1-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/675/2/a/l/1/2'}