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lfunc_lfunctions • Show schema
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{'Lhash': '2220879330607508571354334295053', 'a10': [-51.61395160225576, 29.79932885150268], 'a2': [-2.449489742783178, -1.4142135623730951], 'a3': [0, 0], 'a4': [0, 0], 'a5': [10.535653752852738, -18.24828759089466], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 22.627416997969522], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.019842312531622, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '441.215', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '562722608234879401467277159717', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.449489742783178, 1.4142135623730951], [4.0, 6.928203230275509]], [[1.0, 0], [0, 0]], [[1.0, 0], [-10.535653752852738, 18.24828759089466], [-62.5, -108.25317547305482]], [[1.0, 0], [0, 0]], [[1.0, 0], [-13.47219358530748, 7.7781745930520225], [665.5, 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'0.968053842430609082409192181055581360988335947158950461', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/441/4/p/a/215/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.9680538424306091, 1.1209196217452326, 1.2728450016411996, 1.4220642151181215, 1.5667775298477167, 1.705156828675581, 1.8353532313054197, 1.9555073281769886, 2.0637625029448627, 2.1582817024735803, 2.2372678767462766, 2.298988159767241, 2.3418017008331633, 2.364190887900602, 2.3647955355833687, 2.34244944387474, 2.2962185742119083, 2.2254399411168384, 2.1297601844467224, 2.0091726733305615, 1.8640519021883692, 1.6951838757932334, 1.5037911479750379, 1.2915511808661455, 1.0606067317606784, 0.8135670553624026, 0.5534988323695258, 0.28390590201554355, 0.008697086289216957, -0.26785835422931165, 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'10.20314060044316370133042699405679', '10.77625643975938527543616199113047'], 'prelabel': '2-21e2-21.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.100964841334591, 'root_angle': -0.8827528957359165, 'root_number': '-0.93292539129828042317519157891904600167426089720906541328 - 0.3600697352888053518173335609367142783474201134280481757*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.44137644786795827', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.75196487912967396185299390403', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.05534237248749083467348332384', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.31118664683989206272151536737', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.019842312531622, 'bad_primes': [3, 7], 'central_character': '21.5', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/4/p/a/215/2'], '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': '2-21e2-21.5-c3-0-34', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-21e2-21.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.100964841334591, 'root_angle': -0.44137644786795827, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.75196487912967396185299390403', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2220879330607508571354334295053', 'Lhash_array': ['2220879330607508571354334295053'], 'label': '2-21e2-21.5-c3-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/4/p/a/215/2'}