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lfunc_lfunctions • Show schema
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{'Lhash': '772299072849559773150094118028', 'a10': [0, 0], 'a2': [-32.0, -32.0], 'a3': [748.6975268547109, -748.6975268547109], 'a4': [0, 2048.0], 'a5': [0, 0], 'a6': [-47916.641718701496, 0], 'a7': [121018.4101817431, 121018.4101817431], 'a8': [65536.0, -65536.0], 'a9': [0, -589654.9734367209], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 45.69969086381428, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '6.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [32.0, 32.0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '50.7', 'coefficient_field': 'CDF', 'conductor': 50, 'conductor_radical': 10, 'conjugate': '1912453263954902764511603867678', 'degree': 2, 'euler_factors': [[[1.0, 0], [32.0, 32.0]], [[1.0, 0], [-748.6975268547109, 748.6975268547109], [0, -531441.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-121018.4101817431, -121018.4101817431], [0, 13841287201.0]], [[1.0, 0], [855151.7038889969, 0], [3138428376721.0, 0]], [[1.0, 0], 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'2.178168958158015057805190140653449337604038711278208689', 'load_key': 'CMFs-workshop', 'motivic_weight': 12, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [12], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/50/13/c/c/7/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.08203125', 'prec': 34}, 'plot_values': [2.178168958158015, 1.99699880301487, 1.7727643104164628, 1.508938557908835, 1.2100083583480703, 0.8813839759201006, 0.5292862759506005, 0.16061361883272565, -0.21720874130379306, -0.5963935898534892, -0.9689675062908256, -1.326953644762627, -1.662557530167096, -1.9683517190912674, -2.2374551150953548, -2.463702752072622, -2.64180197049999, -2.767471110687797, -2.8375571344819193, -2.8501289604547515, -2.8045437538468314, -2.701483945907088, -2.5429633603924615, -2.3323014884105917, -2.0740656651422804, -1.7739816499919059, -1.4388138803523616, -1.076217441839959, -0.6945645566538846, 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'10.28553978757166963442562503004370', '11.25197061116816448580576163399939', '13.46662400594209811033884839541298'], 'prelabel': '2-50-5.2-c12-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.760154647921472, 'root_angle': -0.07379180882521663, 'root_number': '0.9732489894677301637880577483081525807410411271519101104 - 0.2297529205473611835239373693814627187159909372855097264*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.036895904412608316', 'prec': 70}, 'spectral_label': 'c12-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.60923654570945186390706323494', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.44205169695443463157956886411', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.07477294724975816556806974815', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 45.69969086381428, 'bad_primes': [2, 5], 'central_character': '5.2', 'conductor': 50, 'conductor_radical': 10, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/50/13/c/c/7/3'], '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': '2-50-5.2-c12-0-6', 'motivic_weight': 12, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [12], 'order_of_vanishing': 0, 'prelabel': '2-50-5.2-c12-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.760154647921472, 'root_angle': -0.036895904412608316, 'self_dual': False, 'spectral_label': 'c12-0', 'z1': {'__RealLiteral__': 0, 'data': '0.60923654570945186390706323494', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '772299072849559773150094118028', 'Lhash_array': ['772299072849559773150094118028'], 'label': '2-50-5.2-c12-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/50/13/c/c/7/3'}