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lfunc_lfunctions • Show schema
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{'Lhash': '3158048706273011418423348683686', 'a10': [39.740852297878796, 5.291695641784708e-60], 'a2': [1.0, 1.7320508075688772], 'a3': [-1.8117376914898995, 4.870072539216931], 'a4': [-2.0, 3.4641016151377544], 'a5': [9.935213074469699, -17.20829382900411], 'a6': [-10.246950765959598, 1.7320508075688772], 'a7': [2.935213074469699, 5.083938176021969], 'a8': [-8.0, 0.0], 'a9': [-20.435213074469697, -17.646587959178472], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0620343801033316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, -1.7320508075688772]]], [3, [[1.0, 0], [1.8117376914898995, -4.870072539216931]]]], 'bad_primes': [2, 3], 'central_character': '18.13', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '5926459684215736846024112186348', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, -1.7320508075688772]], [[1.0, 0], [1.8117376914898995, -4.870072539216931]], 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[1295029.0, 0]], [[1.0, 0], [-825.3635374788638, 1429.5715816281713], [-721448.5, -1249585.457044355]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-18-9.4-c3-0-0', '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/18/4/c/b/13/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [1.169178110274332, 1.1239794115048882, 1.0844403047378142, 1.0483994217987156, 1.0133018084436696, 0.9762654895533054, 0.9341541465005162, 0.8836581630924276, 0.8213890530515007, 0.7439937287930275, 0.6482947132665329, 0.5314603454638503, 0.39120567011803786, 0.2260204353858034, 0.03541578292184658, -0.17982390243327961, -0.4174025895711637, -0.6733108793214382, -0.941687879515705, -1.2147757331658944, -1.482995814453859, -1.7351727573446432, -1.9589262986425753, 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'12.71408902175183919861051798422519', '13.89662624150097310414775033586895', '14.86360813757324261361322118030706', '17.34368284064117606481042047551792', '18.17631068870080158431366727726118'], 'prelabel': '2-18-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0305505228291, 'root_angle': -0.3288229802984496, 'root_number': '0.5122207083627314 - 0.858853855975731*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.164411490149', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.49126116116257301076434845504', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.85119623212478453380424068911', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.35951559821777938586083022979', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0620343801033316, 'bad_primes': [2, 3], 'central_character': '9.4', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/4/c/b/13/1'], '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': '2-18-9.4-c3-0-0', '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': '2-18-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0305505228291, 'root_angle': -0.1644114901492248, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.49126116116257301076434845504', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3158048706273011418423348683686', 'Lhash_array': ['3158048706273011418423348683686'], 'label': '2-18-9.4-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/4/c/b/13/1'}