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lfunc_lfunctions • Show schema
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{'Lhash': '2751552750265936851610195689001', 'a10': 0, 'a2': 1, 'a3': 1, 'a4': 1, 'a5': 0, 'a6': 1, 'a7': -4, 'a8': 1, 'a9': -2, '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, -1, 3], [1], [1, 4, 7], [1, -3, 11], [1, 6, 13], [1, 3, 17], [1, 3, 19], [1, 2, 23], [1, 0, 29], [1, 0, 31], [1, -1], [1, 3, 41], [1, -4, 43], [1, 4, 47], [1, -2, 53], [1, 12, 59], [1, -12, 61], [1, 9, 67], [1, 2, 71], [1, -9, 73], [1, 2, 79], [1, -7, 83], [1, 3, 89], [1, 2, 97], [1, 10, 101], [1, 14, 103], [1, -1, 107], [1, -18, 109], [1, 5, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, -1, 3], 1]], [1], [[[1, 4, 7], 1]], [[[1, -3, 11], 1]], [[[1, 6, 13], 1]], [[[1, 3, 17], 1]], [[[1, 3, 19], 1]], [[[1, 2, 23], 1]], [[[1, 0, 29], 1]], [[[1, 0, 31], 1]], [[[1, -1], 1]], [[[1, 3, 41], 1]], [[[1, -4, 43], 1]], [[[1, 4, 47], 1]], [[[1, -2, 53], 1]], [[[1, 12, 59], 1]], [[[1, -12, 61], 1]], [[[1, 9, 67], 1]], [[[1, 2, 71], 1]], [[[1, -9, 73], 1]], [[[1, 2, 79], 1]], [[[1, -7, 83], 1]], [[[1, 3, 89], 1]], [[[1, 2, 97], 1]], [[[1, 10, 101], 1]], [[[1, 14, 103], 1]], [[[1, -1, 107], 1]], [[[1, -18, 109], 1]], [[[1, 5, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 54, 'label': '2-1850-1.1-c1-0-54', '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/m', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-2.2038832915198663e-59, 0.25504254866021353, 0.5105366559072047, 0.766827570782081, 1.0240547592313853, 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-0.2973711383790361, -0.4583394902297416, -0.5349571841660415, -0.5161814093753161, -0.3988488504203214, -0.1882016660896688], 'positive_zeros': ['2.17059239333815157645595147820971', '2.88961457352644637819188364443709', '3.72752891558989041392547388449934', '4.58444402304127863143112825298306', '5.70532021654462566329979908110772', '6.48907771425825000167110429469391', '7.02816789738378511430085190012782', '8.017294356858624737125820472229805', '9.026698028238458843593900329302215'], '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': 950590029785055198, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.17059239333815157645595147821', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.88961457352644637819188364444', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.72752891558989041392547388450', '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, 1, 1, 0, 1, -4, 1, -2, 0, 3, 1, -6, -4, 0, 1, -3, -2, -3, 0, -4, 3, -2, 1, 0, -6, -5, -4, 0, 0, 0, 1, 3, -3, 0, -2, 1, -3, -6, 0, -3, -4, 4, 3, 0, -2, -4, 1, 9, 0, -3, -6, 2, -5, 0, -4, -3, 0, -12, 0, 12, 0, 8, 1, 0, 3, -9, -3, -2, 0, -2, -2, 9, 1, 0, -3, -12, -6, -2, 0, 1, -3, 7, -4, 0, 4, 0, 3, -3, 0, 24, -2, 0, -4, 0, 1, -2, 9, -6, 0], 'euler11': [1, -3, 11], 'euler13': [1, 6, 13], 'euler17': [1, 3, 17], 'euler19': [1, 3, 19], 'euler2': [1, -1, 0], 'euler23': [1, 2, 23], 'euler29': [1, 0, 29], 'euler3': [1, -1, 3], 'euler31': [1, 0, 31], 'euler37': [1, -1, 0], 'euler41': [1, 3, 41], 'euler43': [1, -4, 43], 'euler47': [1, 4, 47], 'euler5': [1, 0, 0], 'euler53': [1, -2, 53], 'euler59': [1, 12, 59], 'euler61': [1, -12, 61], 'euler67': [1, 9, 67], 'euler7': [1, 4, 7], 'euler71': [1, 2, 71], 'euler73': [1, -9, 73], 'euler79': [1, 2, 79], 'euler83': [1, -7, 83], 'euler89': [1, 3, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, -1, 0], [1, -1, 3], [1, 0, 0], [1, 4, 7], [1, -3, 11], [1, 6, 13], [1, 3, 17], [1, 3, 19], [1, 2, 23], [1, 0, 29], [1, 0, 31], [1, -1, 0], [1, 3, 41], [1, -4, 43], [1, 4, 47], [1, -2, 53], [1, 12, 59], [1, -12, 61], [1, 9, 67], [1, 2, 71], [1, -9, 73], [1, 2, 79], [1, -7, 83], [1, 3, 89], [1, 2, 97]], 'index': 54, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1850/m', 'ModularForm/GL2/Q/holomorphic/1850/2/a/m/1/1', 'ModularForm/GL2/Q/holomorphic/1850/2/a/m'], '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-c1-0-54', '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': 950590029785055198, 'z1': {'__RealLiteral__': 0, 'data': '2.17059239333815157645595147821', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20590954
{'Lhash': '2751552750265936851610195689001', 'Lhash_array': ['2751552750265936851610195689001'], 'label': '2-1850-1.1-c1-0-54', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1850/2/a/m'}
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id: 24554805
{'Lhash': '2751552750265936851610195689001', 'Lhash_array': ['2751552750265936851610195689001'], 'label': '2-1850-1.1-c1-0-54', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1850/2/a/m/1/1'}
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id: 96290
{'Lhash': '950590029785055198', 'Lhash_array': ['950590029785055198'], 'label': '2-1850-1.1-c1-0-54', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1850/m'}