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lfunc_lfunctions • Show schema
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{'Lhash': '1625808370430826410942434464433', 'a10': [1.3336846063687824, 2.31000949950323], 'a2': [-1.9817596639891164, 1.1441694754732588], 'a3': [0.8278627801656245, 1.4339003969420858], 'a4': [1.618247577209504, -2.8028870229521003], 'a5': [0.0, -1.1656355417252635], 'a6': [-3.281250130100248, -1.8944306458918725], 'a7': [-2.58921465123053, -1.4948837758776696], 'a8': [0.0, 2.8295200245136445], 'a9': [0.12928643443288573, -0.2239306731671804], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.217971201457601, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[13, [[1.0, 0], [-3.1505893305298973, -1.753221854287464]]], [31, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [13, 31], 'central_character': '403.218', 'coefficient_field': 'CDF', 'conductor': 403, 'conductor_radical': 403, 'conjugate': '1095164728677700984142308789623', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.9817596639891164, -1.1441694754732588], [1.0, 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[0.08750223937773534, -0.1515583243782917], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 13, 'label': '2-403-13.10-c1-0-13', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/403/2/r/a/218/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7390040945237677, 0.7523679375445983, 0.7534119723058277, 0.7406499039540474, 0.7110817336622489, 0.6610930767584472, 0.5873952254328809, 0.48789196401723955, 0.3624145843935009, 0.21329028581534562, 0.045706697184546424, -0.13217608339423434, -0.30942089645817655, -0.47286550043953346, -0.6080598786613957, -0.7005833271175389, -0.7376900820760082, -0.7101793844397332, -0.6143316597328791, -0.4537040981766254, -0.24054439280903245, 0.003431170934813814, 0.24713261830159072, 0.451251232799121, 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'6.83389247938150759504956287305047', '7.926314939218792876548654375097984', '8.358372278124959655716185769698813', '9.434948587309528394338282558799938', '10.23298091191241681238488793598705', '10.92237398017378437430578273530285'], 'prelabel': '2-403-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7938704528080063, 'root_angle': -0.16761358868320897, 'root_number': '0.864534152326586 - 0.502574073606022*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0838067943416', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28253666281395980563636807502', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.62328275593722210860914867295', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36494574789501896348492442191', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.217971201457601, 'bad_primes': [13, 31], 'central_character': '13.10', 'conductor': 403, 'conductor_radical': 403, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/403/2/r/a/218/5'], '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': '2-403-13.10-c1-0-13', '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': '2-403-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7938704528080063, 'root_angle': -0.08380679434160448, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28253666281395980563636807502', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1625808370430826410942434464433', 'Lhash_array': ['1625808370430826410942434464433'], 'label': '2-403-13.10-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/403/2/r/a/218/5'}