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lfunc_lfunctions • Show schema
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{'Lhash': '1124245103021645261695093115488', 'a10': [1.4142135623730951, 0.0], 'a2': [-0.41421356237309503, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.82842712474619, 0.0], 'a5': [-3.414213562373095, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [1.5857864376269049, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '441.1', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '1124245103021645261695093115488', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.41421356237309503, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.414213562373095, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.0, 0], [11.0, 0]], [[1.0, 0], [-2.585786437626905, 0], [13.0, 0]], [[1.0, 0], [-2.242640687119285, 0], [17.0, 0]], [[1.0, 0], 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'6.66328616045060353467405089350055', '7.65630259062102721473457234018616', '8.520270031082421588158231239740247', '9.005376370676956116405339931167933', '10.28656416713327785743945911649947', '11.08816099052193730586026017415729'], 'prelabel': '2-21e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, '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': '0.886873009659944755673861585793', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.38373017834395905072088271255', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.15787096548369957526349467029', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/2/a/i/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': '2-21e2-1.1-c1-0-1', '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': '2-21e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.886873009659944755673861585793', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1124245103021645261695093115488', 'Lhash_array': ['1124245103021645261695093115488'], 'label': '2-21e2-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/2/a/i/1/1'}