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lfunc_lfunctions • Show schema
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{'Lhash': '2213154760384711576038592147322', 'a10': [0.5, -0.13397459621556135], 'a2': [0.9659258262890683, -0.25881904510252074], 'a3': [0.0, 0.0], 'a4': [0.8660254037844386, -0.5], 'a5': [0.5176380902050415, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.401374555473471, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9659258262890683, 0.25881904510252074]]], [3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3, 13], 'central_character': '2808.2755', 'coefficient_field': 'CDF', 'conductor': 2808, 'conductor_radical': 78, 'conjugate': '1677132479560950505032414047836', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9659258262890683, 0.25881904510252074]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 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'6.74248279079678015072820137058061', '7.42054882081458120179268231687367', '8.044024529312454462370458196506788', '9.058485176878098029211367290214256'], 'prelabel': '2-2808-104.51-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1837966698185423, 'root_angle': 0.125, 'root_number': '0.70710678118654752440084436210459 + 0.70710678118654752440084436210459*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74587126767127505128596675033', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.54044028150459939190878835658', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.58688824961936792059569258256', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.401374555473471, 'bad_primes': [2, 3, 13], 'central_character': '104.51', 'conductor': 2808, 'conductor_radical': 78, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2808/1/o/a/2755/7'], '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': '2-2808-104.51-c0-0-7', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2808-104.51-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1837966698185423, 'root_angle': 0.125, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.74587126767127505128596675033', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2213154760384711576038592147322', 'Lhash_array': ['2213154760384711576038592147322'], 'factors': ['2-2808-104.51-c0-0-7'], 'label': '2-2808-104.51-c0-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2808/1/o/a/2755/7'}