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lfunc_lfunctions • Show schema
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{'Lhash': '2085465294911793695925531974705', 'a10': 0, 'a2': 1, 'a3': -2, 'a4': 1, 'a5': 0, 'a6': -2, 'a7': -1, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.772324373936879, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [5, [1]], [37, [1, -1]]], 'bad_primes': [2, 5, 37], 'central_character': '1850.1', 'coefficient_field': '1.1.1.1', 'conductor': 1850, 'conductor_radical': 370, 'degree': 2, 'euler_factors': [[1, -1], [1, 2, 3], [1], [1, 1, 7], [1, -3, 11], [1, 0, 13], [1, 3, 17], [1, 6, 19], [1, 2, 23], [1, 3, 29], [1, -3, 31], [1, -1], [1, -3, 41], [1, -1, 43], [1, 4, 47], [1, 13, 53], [1, 0, 59], [1, 15, 61], [1, 0, 67], [1, 2, 71], [1, 0, 73], [1, 8, 79], [1, -4, 83], [1, 18, 89], [1, -7, 97], [1, 10, 101], [1, 8, 103], [1, 2, 107], [1, 3, 109], [1, -7, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, 2, 3], 1]], [1], [[[1, 1, 7], 1]], [[[1, -3, 11], 1]], [[[1, 0, 13], 1]], [[[1, 3, 17], 1]], [[[1, 6, 19], 1]], [[[1, 2, 23], 1]], [[[1, 3, 29], 1]], [[[1, -3, 31], 1]], [[[1, -1], 1]], [[[1, -3, 41], 1]], [[[1, -1, 43], 1]], [[[1, 4, 47], 1]], [[[1, 13, 53], 1]], [[[1, 0, 59], 1]], [[[1, 15, 61], 1]], [[[1, 0, 67], 1]], [[[1, 2, 71], 1]], [[[1, 0, 73], 1]], [[[1, 8, 79], 1]], [[[1, -4, 83], 1]], [[[1, 18, 89], 1]], [[[1, -7, 97], 1]], [[[1, 10, 101], 1]], [[[1, 8, 103], 1]], [[[1, 2, 107], 1]], [[[1, 3, 109], 1]], [[[1, -7, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 46, 'label': '2-1850-1.1-c1-0-46', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1850/2/a/i', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.1036128656831868e-60, 0.15809811330731463, 0.316068704983159, 0.4737410315610808, 0.6308601337560866, 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0.4979387605014335, 0.6304737968626474, 0.7016587304166889, 0.7027686488075321, 0.628811290074157, 0.4789241765311695, 0.2565529871399944, -0.030603365000503705], 'positive_zeros': ['1.64514204035112192009306844051742', '2.94631810557103912586946477936331', '4.14074597563837066006181115129103', '4.68567966081196923689329880264482', '5.75894180480402141133249940840118', '6.38244555304273679459795010368009', '6.74330103812297173688363684264665', '7.940617253362879027486346170110295', '8.909285651436971781795443789502230'], 'prelabel': '2-1850-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.8434781609808684, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1013534411075492212, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.64514204035112192009306844052', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.94631810557103912586946477936', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.14074597563837066006181115129', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.772324373936879, 'bad_primes': [2, 5, 37], 'central_character': '1.1', 'conductor': 1850, 'conductor_radical': 370, 'degree': 2, 'dirichlet_coefficients': [1, 1, -2, 1, 0, -2, -1, 1, 1, 0, 3, -2, 0, -1, 0, 1, -3, 1, -6, 0, 2, 3, -2, -2, 0, 0, 4, -1, -3, 0, 3, 1, -6, -3, 0, 1, 1, -6, 0, 0, 3, 2, 1, 3, 0, -2, -4, -2, -6, 0, 6, 0, -13, 4, 0, -1, 12, -3, 0, 0, -15, 3, -1, 1, 0, -6, 0, -3, 4, 0, -2, 1, 0, 1, 0, -6, -3, 0, -8, 0, -11, 3, 4, 2, 0, 1, 6, 3, -18, 0, 0, -2, -6, -4, 0, -2, 7, -6, 3, 0], 'euler11': [1, -3, 11], 'euler13': [1, 0, 13], 'euler17': [1, 3, 17], 'euler19': [1, 6, 19], 'euler2': [1, -1, 0], 'euler23': [1, 2, 23], 'euler29': [1, 3, 29], 'euler3': [1, 2, 3], 'euler31': [1, -3, 31], 'euler37': [1, -1, 0], 'euler41': [1, -3, 41], 'euler43': [1, -1, 43], 'euler47': [1, 4, 47], 'euler5': [1, 0, 0], 'euler53': [1, 13, 53], 'euler59': [1, 0, 59], 'euler61': [1, 15, 61], 'euler67': [1, 0, 67], 'euler7': [1, 1, 7], 'euler71': [1, 2, 71], 'euler73': [1, 0, 73], 'euler79': [1, 8, 79], 'euler83': [1, -4, 83], 'euler89': [1, 18, 89], 'euler97': [1, -7, 97], 'euler_factors': [[1, -1, 0], [1, 2, 3], [1, 0, 0], [1, 1, 7], [1, -3, 11], [1, 0, 13], [1, 3, 17], [1, 6, 19], [1, 2, 23], [1, 3, 29], [1, -3, 31], [1, -1, 0], [1, -3, 41], [1, -1, 43], [1, 4, 47], [1, 13, 53], [1, 0, 59], [1, 15, 61], [1, 0, 67], [1, 2, 71], [1, 0, 73], [1, 8, 79], [1, -4, 83], [1, 18, 89], [1, -7, 97]], 'index': 46, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1850/i', 'ModularForm/GL2/Q/holomorphic/1850/2/a/i/1/1', 'ModularForm/GL2/Q/holomorphic/1850/2/a/i'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-1850-1.1-c1-0-46', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1850-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.8434781609808684, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1013534411075492212, 'z1': {'__RealLiteral__': 0, 'data': '1.64514204035112192009306844052', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20590950
{'Lhash': '2085465294911793695925531974705', 'Lhash_array': ['2085465294911793695925531974705'], 'label': '2-1850-1.1-c1-0-46', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1850/2/a/i'}
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id: 24554801
{'Lhash': '2085465294911793695925531974705', 'Lhash_array': ['2085465294911793695925531974705'], 'label': '2-1850-1.1-c1-0-46', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1850/2/a/i/1/1'}
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id: 39814
{'Lhash': '1013534411075492212', 'Lhash_array': ['1013534411075492212'], 'label': '2-1850-1.1-c1-0-46', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1850/i'}