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lfunc_lfunctions • Show schema
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{'Lhash': '2843830357802767257902729835667', 'a10': [-2.7254487353011068, 0.0], 'a2': [-1.0, 0.0], 'a3': [-0.5239763970818659, 0.0], 'a4': [1.0, 0.0], 'a5': [2.7254487353011068, 0.0], 'a6': [0.5239763970818659, 0.0], 'a7': [-4.677495941137375, 0.0], 'a8': [-1.0, 0.0], 'a9': [-2.7254487353011068, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3377468044895218, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 11, 19], 'central_character': '418.1', 'coefficient_field': 'CDF', 'conductor': 418, 'conductor_radical': 418, 'conjugate': '2843830357802767257902729835667', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [0.5239763970818659, 0], [3.0, 0]], [[1.0, 0], [-2.7254487353011068, 0], [5.0, 0]], [[1.0, 0], [4.677495941137375, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.6774959411373747, 0], [13.0, 0]], 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'6.77147420273669735592495256262944', '8.104237365947781713185799950728250', '9.395386306719266426829043607877564', '9.632150176985009153552023325162979', '10.47237483429772476526265485732630'], 'prelabel': '2-418-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8269501373845762, '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': '2.24338659035128487223618747892', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.28119770158828625991758593167', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.33168575139771341337615999557', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.3377468044895218, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 418, 'conductor_radical': 418, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/418/2/a/g/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': '2-418-1.1-c1-0-12', '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': '2-418-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8269501373845762, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.24338659035128487223618747892', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2843830357802767257902729835667', 'Lhash_array': ['2843830357802767257902729835667'], 'label': '2-418-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/418/2/a/g/1/2'}