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lfunc_lfunctions • Show schema
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{'Lhash': '1691003380467369123706709943967', 'a10': [-1.0, 0.0], 'a2': [1.0, 0.0], 'a3': [-0.6180339887498949, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [-0.6180339887498949, 0.0], 'a7': [-1.618033988749895, 0.0], 'a8': [1.0, 0.0], 'a9': [-2.618033988749895, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.240862669257346, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 23], 'central_character': '5290.1', 'coefficient_field': 'CDF', 'conductor': 5290, 'conductor_radical': 230, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.6180339887498949, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.618033988749895, 0], [7.0, 0]], [[1.0, 0], [3.8541019662496847, 0], [11.0, 0]], [[1.0, 0], [-4.0901699437494745, 0], [13.0, 0]], [[1.0, 0], [-5.0901699437494745, 0], [17.0, 0]], [[1.0, 0], 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[[1.0, 0], [18.94427190999916, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 126, 'label': '2-5290-1.1-c1-0-126', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/5290/2/a/o/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.161953633913135e-60, 0.21055388315119275, 0.4200643919070689, 0.6274431981409644, 0.8315149771290798, 1.0309809834872645, 1.2243905744693628, 1.4101225004276257, 1.5863772018307747, 1.7511807575665732, 1.9024005681492286, 2.037772362683362, 2.1549377064337167, 2.251490858847582, 2.3250335821018906, 2.3732363146522473, 2.3939039886807802, 2.385044672460022, 2.34493914966397, 2.272209502784233, 2.165884746001531, 2.025461556039144, 1.8509581815994776, 1.642959677887134, 1.4026527175131582, 1.1318483772140882, 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'5.54381359289116914041628820765755', '6.15620996062020129395201056661685', '7.08270744356990329242129282344530', '7.75274728439861315120651588332664'], 'prelabel': '2-5290-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.499297090398111, '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': '1.33396645744727983997076155033', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.80966264078545540705206855109', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.25218831129758247552551985199', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.240862669257346, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 5290, 'conductor_radical': 230, 'degree': 2, 'index': 126, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5290/2/a/o/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': '2-5290-1.1-c1-0-126', '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': '2-5290-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.499297090398111, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33396645744727983997076155033', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1691003380467369123706709943967', 'Lhash_array': ['1691003380467369123706709943967'], 'label': '2-5290-1.1-c1-0-126', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5290/2/a/o/1/1'}