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lfunc_lfunctions • Show schema
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{'Lhash': '689316919001521510791617628451', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.3090169943749475, 2.267283942228512], 'a4': [0, 0], 'a5': [2.618033988749895, 0], 'a6': [0, 0], 'a7': [0.5, 0.8660254037844386], 'a8': [0, 0], 'a9': [-1.9270509831248424, -3.337750211547782], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.62621853429843, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.5, -0.8660254037844386]]], [13, [[1.0, 0], [2.5, -2.598076211353316]]]], 'bad_primes': [2, 7, 13], 'central_character': '1456.113', 'coefficient_field': 'CDF', 'conductor': 1456, 'conductor_radical': 182, 'conjugate': '2057037080029733030556950409291', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.3090169943749475, -2.267283942228512], [-1.5, -2.598076211353316]], [[1.0, 0], [-2.618033988749895, 0], [5.0, 0]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-0.9270509831248422, 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[-33.5, -58.023702053557386]], [[1.0, 0], [7.0901699437494745, 12.280534576871858], [-35.5, 61.48780366869514]], [[1.0, 0], [2.0, 0], [73.0, 0]], [[1.0, 0], [4.0, 0], [79.0, 0]], [[1.0, 0], [6.708203932499369, 0], [83.0, 0]], [[1.0, 0], [2.4549150281252627, -4.252037556977335], [-44.5, -77.07626093681505]], [[1.0, 0], [9.427050983124841, 16.328131268314362], [-48.5, 84.00446416709055]], [[1.0, 0], [-5.781152949374527, 10.013250634643345], [-50.5, -87.4685657822283]], [[1.0, 0], [-8.70820393249937, 0], [103.0, 0]], [[1.0, 0], [1.6909830056250525, -2.9288684804781195], [-53.5, -92.66471820493493]], [[1.0, 0], [2.708203932499369, 0], [109.0, 0]], [[1.0, 0], [0.7360679774997897, 1.274907134854101], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-1456-13.9-c1-0-11', 'leading_term': '1.2639855846567499265730709469395676885471389249941471162', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': 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False, 'root_analytic_conductor': 3.4097241141034313, 'root_angle': -0.41870761805923334, 'root_number': '-0.87236585943566271307206279130657783064408656301463933702 - 0.4888535642614028900637260750591766424339409441677279794*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4187076180592334', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.54377516870769913214941928173', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.79674521092784992695523399081', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.49150510071916518720464521296', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.62621853429843, 'bad_primes': [2, 7, 13], 'central_character': '13.9', 'conductor': 1456, 'conductor_radical': 182, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1456/2/s/h/113/1'], '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': '2-1456-13.9-c1-0-11', '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': '2-1456-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4097241141034313, 'root_angle': -0.41870761805923334, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.54377516870769913214941928173', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '689316919001521510791617628451', 'Lhash_array': ['689316919001521510791617628451'], 'factors': ['2-1456-13.9-c1-0-11'], 'label': '2-1456-13.9-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1456/2/s/h/113/1'}