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lfunc_lfunctions • Show schema
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{'Lhash': '2479485006306379671267234915559', 'a10': [0.6209472207749499, -0.3585040450669673], 'a2': [0.24617959695923242, -0.0659636241982456], 'a3': [1.7274045222312513, 0.12678176751813616], 'a4': [-1.6757976133272345, 0.9675222031618113], 'a5': [2.7174374469596096, -0.7281351693949193], 'a6': [0.43361473393620054, -0.08273477831341837], 'a7': [1.4117885518439672, -2.2375998491424496], 'a8': [-0.7091578555432915, 0.7091578555432915], 'a9': [2.9678527668499544, 0.4380067970945991], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.7274045222312513, -0.12678176751813616]]], [7, [[1.0, 0], [-1.4117885518439672, 2.2375998491424496]]], [13, [[1.0, 0], [3.472955570146415, -0.968803183205437]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.44', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': 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-0.49450934842029826, -0.054794089542416324], 'positive_zeros': ['1.95596878655677683248455759078426', '3.08453780406649696290071720891354', '5.05910572038100561679066655039719', '5.42980644895708916988100424097003', '7.09480867033839064867125404846907', '8.153257766378407903266594112647348', '9.416698729625160102470949942110257', '9.586875601777155021004072048623190', '10.60945005198824552304685675721524', '12.26010906028898045273491375979921'], 'prelabel': '2-273-273.44-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.002134048352892351, 'root_number': '0.9999775261936819 + 0.0067042604039839115*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00106702417645', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.95596878655677683248455759078', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.08453780406649696290071720891', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.05910572038100561679066655040', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '273.44', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/cd/e/44/15'], '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': '2-273-273.44-c1-0-21', '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': '2-273-273.44-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.0010670241764461756, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.95596878655677683248455759078', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2479485006306379671267234915559', 'Lhash_array': ['2479485006306379671267234915559'], 'label': '2-273-273.44-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/cd/e/44/15'}