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lfunc_lfunctions • Show schema
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{'Lhash': '1269497699976924409851317427243', 'a10': [1.942748736788282, 1.1071257135969403], 'a2': [-0.9659258262890683, -0.25881904510252074], 'a3': [-0.7935191512253821, 1.5395867486564534], 'a4': [0.8660254037844386, 0.5], 'a5': [-2.163096398855872, -0.5665809467823273], 'a6': [1.1649550139633353, -1.2817487333489685], 'a7': [4.162316159894334, -1.1152892536866985], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [-1.7406547132770982, -2.443383140063429], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9659258262890683, 0.25881904510252074]]], [3, [[1.0, 0], [0.7935191512253821, -1.5395867486564534]]], [5, [[1.0, 0], [2.163096398855872, 0.5665809467823273]]], [13, [[1.0, 0], [0.19606526783845915, 3.600216439430751]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.23', 'coefficient_field': 'CDF', 'conductor': 390, 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'positive_zeros': ['1.00145710477978904770983816990828', '2.49589820973484247502004972210347', '4.44731566195329717675422015324436', '5.59817263194082048117134222259551', '6.85759181747915496936392214567466', '7.42981386707901962782994804000797', '8.561727688503838460267415712043285', '8.809689256882801656092806594851871', '10.86550576329943493847803055462164', '11.20285159320575053173491736572663'], 'prelabel': '2-390-195.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.18733424998478598, 'root_number': '0.831758795556591 - 0.5551371956681059*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0936671249924', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00145710477978904770983816991', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49589820973484247502004972210', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.44731566195329717675422015324', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'bad_primes': [2, 3, 5, 13], 'central_character': '195.23', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/be/b/23/4'], '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': '2-390-195.23-c1-0-7', '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': '2-390-195.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.09366712499239299, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00145710477978904770983816991', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1269497699976924409851317427243', 'Lhash_array': ['1269497699976924409851317427243'], 'label': '2-390-195.23-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/be/b/23/4'}