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lfunc_lfunctions • Show schema
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{'Lhash': '2096182675287783071172836196638', 'a10': [0.8090169943749475, 0.5877852522924731], 'a2': [0.9135454576426009, -0.4067366430758002], 'a3': [0.6691306063588582, 0.7431448254773942], 'a4': [0.6691306063588582, -0.7431448254773942], 'a5': [0.5, 0.8660254037844386], 'a6': [0.9135454576426009, 0.4067366430758002], 'a7': [0.0, 0.0], 'a8': [0.30901699437494745, -0.9510565162951535], '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], [-0.9135454576426009, 0.4067366430758002]]], [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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['1.65359656273612280650722308997183', '2.41537329065942499066386119931410', '3.66335536001571587517862164463034', '4.41045299520450373444235841119288', '5.47750450488152572223947124785967', '6.20260919227504814693174953208790', '6.89291801217020875495897043385997', '7.78998164690705058683144379477422', '8.560431073842139997435942583915748', '8.958439870875616657013996740340749'], 'prelabel': '2-1860-1860.1499-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9634629850167491, 'root_angle': -0.046819901161216974, 'root_number': '0.95704077384101234589432180525027 - 0.28995337074398058988709267684908*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.04681990116121698', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.65359656273612280650722308997', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.41537329065942499066386119931', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.66335536001571587517862164463', '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': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1860/1/df/d/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-c0-0-2', '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': -0.046819901161216974, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.65359656273612280650722308997', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2096182675287783071172836196638', 'Lhash_array': ['2096182675287783071172836196638'], 'factors': ['2-1860-1860.1499-c0-0-2'], 'label': '2-1860-1860.1499-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1860/1/df/d/1499/1'}