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lfunc_lfunctions • Show schema
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{'Lhash': '2209638383933003766272779724237', 'a10': [-0.6691306063588582, -0.7431448254773942], 'a2': [0.9781476007338057, -0.20791169081775934], 'a3': [0.6691306063588582, 0.7431448254773942], 'a4': [0.9135454576426009, -0.4067366430758002], 'a5': [-0.5, -0.8660254037844386], 'a6': [0.8090169943749475, 0.5877852522924731], 'a7': [0.0, 0.0], 'a8': [0.8090169943749475, -0.5877852522924731], 'a9': [-0.10452846326765347, 0.9945218953682733], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9282609234973845, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9781476007338057, 0.20791169081775934]]], [3, [[1.0, 0], [-0.6691306063588582, -0.7431448254773942]]], [5, [[1.0, 0], [0.5, 0.8660254037844386]]], [31, [[1.0, 0], [-0.30901699437494745, -0.9510565162951535]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '1860.1499', 'coefficient_field': 'CDF', 'conductor': 1860, 'conductor_radical': 930, 'conjugate': 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'positive_zeros': ['1.74309733576048297897044089319351', '2.84690349760760379781477373954666', '3.44091315379379180568924306985775', '4.28655182851154061886505240986690', '5.64523310680757892470172297168247', '6.24596741067182865234038593892354', '7.18123769321617250242938318723743', '7.72120102922636273285370224570151', '8.112087461092456936938964226056489', '9.524012143339665762780970115520421'], 'prelabel': '2-1860-1860.1499-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9634629850167491, 'root_angle': 0.01984676550544969, 'root_number': '0.99223491238613613050415204504255 + 0.12437796686743499309531955756122*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.019846765505449688', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74309733576048297897044089319', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.84690349760760379781477373955', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44091315379379180568924306986', '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': '1860.1499', 'conductor': 1860, 'conductor_radical': 930, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1860/1/df/b/1499/1'], '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': '2-1860-1860.1499-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': '2-1860-1860.1499-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9634629850167491, 'root_angle': 0.01984676550544969, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.74309733576048297897044089319', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2209638383933003766272779724237', 'Lhash_array': ['2209638383933003766272779724237'], 'factors': ['2-1860-1860.1499-c0-0-3'], 'label': '2-1860-1860.1499-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1860/1/df/b/1499/1'}