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lfunc_lfunctions • Show schema
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{'Lhash': '1469586562518409171585608746444', 'a10': [0.6743059820807961, -1.1679322208115677], 'a2': [0.8660254037844386, 0.5], 'a3': [0, 0], 'a4': [0.5, 0.8660254037844386], 'a5': [0, -1.3486119641615921], 'a6': [0, 0], 'a7': [-0.8660254037844386, 0.5], 'a8': [0, 1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.079495851085733, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.8660254037844386, -0.5]]], [13, [[1.0, 0], [0.34304320035913033, 3.589195085626771]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '1638.1135', 'coefficient_field': 'CDF', 'conductor': 1638, 'conductor_radical': 546, 'conjugate': '1248786044872849204174329628425', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.3486119641615921], [-5.0, 0]], [[1.0, 0], [0.8660254037844386, -0.5]], 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'8.758973494537578924078141594807892', '9.557942036090105109471542971353702'], 'prelabel': '2-1638-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6165585645867444, 'root_angle': -0.03441275915649728, 'root_number': '0.99416170954773658764415522046119957902627860598423576480 - 0.1079003951295908581933716014602459787035319972858770363*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.01720637957824864', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.15929938600890731764833332438', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.54071656864411538026030260544', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36121877616113845859014060555', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.079495851085733, 'bad_primes': [2, 3, 7, 13], 'central_character': '13.4', 'conductor': 1638, 'conductor_radical': 546, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1638/2/bj/h/1135/6'], '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': '2-1638-13.4-c1-0-21', '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': '2-1638-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6165585645867444, 'root_angle': -0.01720637957824864, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.15929938600890731764833332438', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1469586562518409171585608746444', 'Lhash_array': ['1469586562518409171585608746444'], 'label': '2-1638-13.4-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1638/2/bj/h/1135/6'}