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lfunc_lfunctions • Show schema
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{'Lhash': '3373884374868521914217272510964', 'a10': [0.30901699437494745, -0.9510565162951535], 'a2': [0.30901699437494745, 0.9510565162951535], 'a3': [0.0, 0.0], 'a4': [-0.8090169943749475, 0.5877852522924731], 'a5': [-0.8090169943749475, -0.5877852522924731], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.8090169943749475, -0.5877852522924731], 'a9': [0.30901699437494745, -0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.04990650126330024, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.30901699437494745, -0.9510565162951535]]], [5, [[1.0, 0], [0.8090169943749475, 0.5877852522924731]]]], 'bad_primes': [2, 5], 'central_character': '100.31', 'coefficient_field': 'CDF', 'conductor': 100, 'conductor_radical': 10, 'conjugate': '4851415872363218420561962287951', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [-0.30901699437494745, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-10e2-100.31-c0-0-0', 'leading_term': '0.55342604276221075297895213913938', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/100/1/j/a/31/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.08203125', 'prec': 34}, 'plot_values': [0.5534260427622107, 0.5516420037898112, 0.5644457298633254, 0.5897669493269715, 0.6252260725302948, 0.6685090612091592, 0.7175616990630748, 0.7706253681709435, 0.826187615245217, 0.8829065314569341, 0.9395399049435439, 0.9948904582787725, 1.0477688139910049, 1.0969722375023438, 1.1412764237112847, 1.1794378444658953, 1.2102046720095925, 1.2323347445451074, 1.2446193625860573, 1.245911896815316, 1.2351602725840094, 1.2114423999044728, 1.1740035652671568, 1.1222947135118755, 1.0560104416175078, 0.9751254163936278, 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'10.72134589933074432226622561991973', '11.84084510380340478198286773063701', '12.83333147423805482282199149653416', '13.73966495852089220025482417048723'], 'prelabel': '2-10e2-100.31-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.2233976303887314, 'root_angle': -0.32, 'root_number': '0.53582679497899661827130876786751 - 0.84432792550201507854855806396698*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.16', 'prec': 17}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.66152548206980973020188319867', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.14002826679925869875833378269', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.52389601233870343120666487150', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.04990650126330024, 'bad_primes': [2, 5], 'central_character': '100.31', 'conductor': 100, 'conductor_radical': 10, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/100/1/j/a/31/1'], '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': '2-10e2-100.31-c0-0-0', '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': '2-10e2-100.31-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.2233976303887314, 'root_angle': -0.16, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.66152548206980973020188319867', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3373884374868521914217272510964', 'Lhash_array': ['3373884374868521914217272510964'], 'label': '2-10e2-100.31-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/100/1/j/a/31/1'}