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lfunc_lfunctions • Show schema
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{'Lhash': '1814830576796804473319339820739', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.137261107234623, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -1]], [19, [1, -1]]], 'bad_primes': [2, 5, 19], 'central_character': '1520.1', 'coefficient_field': '1.1.1.1', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[1], [1, 2, 3], [1, -1], [1, 4, 7], [1, -4, 11], [1, 0, 13], [1, -6, 17], [1, -1], [1, 8, 23], [1, 6, 29], [1, -8, 31], [1, 8, 37], [1, 2, 41], [1, 0, 43], [1, 12, 47], [1, -4, 53], [1, 8, 59], [1, 14, 61], [1, -2, 67], [1, -8, 71], [1, 2, 73], [1, 4, 79], [1, 12, 83], [1, -6, 89], [1, 0, 97], [1, 6, 101], [1, -6, 103], [1, 18, 107], [1, 2, 109], [1, 16, 113]], 'euler_factors_factorization': [[1], [[[1, 2, 3], 1]], [[[1, -1], 1]], [[[1, 4, 7], 1]], [[[1, -4, 11], 1]], [[[1, 0, 13], 1]], [[[1, -6, 17], 1]], [[[1, -1], 1]], [[[1, 8, 23], 1]], [[[1, 6, 29], 1]], [[[1, -8, 31], 1]], [[[1, 8, 37], 1]], [[[1, 2, 41], 1]], [[[1, 0, 43], 1]], [[[1, 12, 47], 1]], [[[1, -4, 53], 1]], [[[1, 8, 59], 1]], [[[1, 14, 61], 1]], [[[1, -2, 67], 1]], [[[1, -8, 71], 1]], [[[1, 2, 73], 1]], [[[1, 4, 79], 1]], [[[1, 12, 83], 1]], [[[1, -6, 89], 1]], [[[1, 0, 97], 1]], [[[1, 6, 101], 1]], [[[1, -6, 103], 1]], [[[1, 18, 107], 1]], [[[1, 2, 109], 1]], [[[1, 16, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 22, 'label': '2-1520-1.1-c1-0-22', '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/1520/2/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-8.228479185765611e-61, 0.11913876784051736, 0.2379082578680743, 0.3558750854181423, 0.47248200601434137, 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4.0590228746516965, 3.7458338285972834, 3.235079848115996, 2.5476112034040184, 1.7146825629215083, 0.7760974515273746, -0.22219063885314025, -1.230866574014741], 'positive_zeros': ['1.43164889163469816022501322948697', '3.07425032684048770058081362283557', '3.89039366794407092271004025253966', '5.14236160489505260986626044288378', '6.07553649243771927211326383485146', '6.26604533373139617436495529729271', '7.15092239567899718438965748252261', '8.306558588442832701284063292787957', '9.414389171153941052152571176805851'], 'prelabel': '2-1520-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.483857216826577, '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': 615700250989792885, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.43164889163469816022501322949', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07425032684048770058081362284', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.89039366794407092271004025254', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.137261107234623, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, 0, 1, 0, -4, 0, 1, 0, 4, 0, 0, 0, -2, 0, 6, 0, 1, 0, 8, 0, -8, 0, 1, 0, 4, 0, -6, 0, 8, 0, -8, 0, -4, 0, -8, 0, 0, 0, -2, 0, 0, 0, 1, 0, -12, 0, 9, 0, -12, 0, 4, 0, 4, 0, -2, 0, -8, 0, -14, 0, -4, 0, 0, 0, 2, 0, 16, 0, 8, 0, -2, 0, -2, 0, -16, 0, -4, 0, -11, 0, -12, 0, 6, 0, 12, 0, 6, 0, 0, 0, -16, 0, 1, 0, 0, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, 0, 13], 'euler17': [1, -6, 17], 'euler19': [1, -1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, 6, 29], 'euler3': [1, 2, 3], 'euler31': [1, -8, 31], 'euler37': [1, 8, 37], 'euler41': [1, 2, 41], 'euler43': [1, 0, 43], 'euler47': [1, 12, 47], 'euler5': [1, -1, 0], 'euler53': [1, -4, 53], 'euler59': [1, 8, 59], 'euler61': [1, 14, 61], 'euler67': [1, -2, 67], 'euler7': [1, 4, 7], 'euler71': [1, -8, 71], 'euler73': [1, 2, 73], 'euler79': [1, 4, 79], 'euler83': [1, 12, 83], 'euler89': [1, -6, 89], 'euler97': [1, 0, 97], 'euler_factors': [[1, 0, 0], [1, 2, 3], [1, -1, 0], [1, 4, 7], [1, -4, 11], [1, 0, 13], [1, -6, 17], [1, -1, 0], [1, 8, 23], [1, 6, 29], [1, -8, 31], [1, 8, 37], [1, 2, 41], [1, 0, 43], [1, 12, 47], [1, -4, 53], [1, 8, 59], [1, 14, 61], [1, -2, 67], [1, -8, 71], [1, 2, 73], [1, 4, 79], [1, 12, 83], [1, -6, 89], [1, 0, 97]], 'index': 22, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1520/c', 'ModularForm/GL2/Q/holomorphic/1520/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/1520/2/a/c'], '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': '2-1520-1.1-c1-0-22', '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': '2-1520-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 615700250989792885, 'z1': {'__RealLiteral__': 0, 'data': '1.43164889163469816022501322949', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20651897
{'Lhash': '1814830576796804473319339820739', 'Lhash_array': ['1814830576796804473319339820739'], 'label': '2-1520-1.1-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/a/c'}
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id: 24553457
{'Lhash': '1814830576796804473319339820739', 'Lhash_array': ['1814830576796804473319339820739'], 'label': '2-1520-1.1-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/a/c/1/1'}
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id: 88813
{'Lhash': '615700250989792885', 'Lhash_array': ['615700250989792885'], 'label': '2-1520-1.1-c1-0-22', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1520/c'}