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lfunc_lfunctions • Show schema
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{'Lhash': '2065351048275173658100430339917', 'a10': [0.8090169943749475, -0.5877852522924731], 'a2': [0.8090169943749475, -0.5877852522924731], 'a3': [-0.8090169943749475, 0.5877852522924731], 'a4': [0.30901699437494745, -0.9510565162951535], 'a5': [1.0, 0.0], 'a6': [-0.30901699437494745, 0.9510565162951535], 'a7': [0.0, 0.0], 'a8': [-0.30901699437494745, -0.9510565162951535], 'a9': [0.30901699437494745, -0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9282609234973845, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8090169943749475, 0.5877852522924731]]], [3, [[1.0, 0], [0.8090169943749475, -0.5877852522924731]]], [5, [[1.0, 0], [-1.0, 0]]], [31, [[1.0, 0], [0.8090169943749475, 0.5877852522924731]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '1860.959', 'coefficient_field': 'CDF', 'conductor': 1860, 'conductor_radical': 930, 'conjugate': '1497118684622948430008620086843', 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[-0.6180339887498949, -1.902113032590307], [-0.8090169943749475, 0.5877852522924731]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-1860-1860.959-c0-0-3', 'leading_term': '1.6439712468260242026412183788130', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1860/1/bt/c/959/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.6439712468260241, 1.6889887826668204, 1.7505765947522602, 1.8278477322217177, 1.9186559025398127, 2.0199035699795553, 2.127868272127702, 2.2384792720050473, 2.347520865903537, 2.4507697104202055, 2.544086226559931, 2.6234804179534432, 2.685167481955824, 2.7256228509073517, 2.7416415882704466, 2.7304037187040513, 2.6895448669161537, 2.6172301860859717, 2.512228700059397, 2.3739846803149787, 2.202682418069367, 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'5.07485738999547837359178308861042', '5.54766106493140797177295970345265', '6.27763249087299273818585944963648', '6.92232958080548755146923910896743', '7.69725640359054565877162172788467', '8.540003043577932846906887954625085', '9.539166228349723488487570672019605'], 'prelabel': '2-1860-1860.959-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9634629850167491, 'root_angle': 0.15364727042335866, 'root_number': '0.56909272118240398061655780599830 + 0.82227335764769042142673341348985*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.15364727042335866', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.62927469754151914494956834961', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.65440979544589419323736901972', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.92931043357240934054427857093', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9282609234973845, 'bad_primes': [2, 3, 5, 31], 'central_character': '1860.959', 'conductor': 1860, 'conductor_radical': 930, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1860/1/bt/c/959/1'], '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': '2-1860-1860.959-c0-0-3', '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': '2-1860-1860.959-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9634629850167491, 'root_angle': 0.15364727042335866, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.62927469754151914494956834961', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2065351048275173658100430339917', 'Lhash_array': ['2065351048275173658100430339917'], 'factors': ['2-1860-1860.959-c0-0-3'], 'label': '2-1860-1860.959-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1860/1/bt/c/959/1'}