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lfunc_lfunctions • Show schema
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{'Lhash': '1809379137697925425371521585675', 'a10': 0, 'a2': -1, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 3, 'a8': 3, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.762974500266903, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [11, [1, 1]]], 'bad_primes': [3, 5, 11], 'central_character': '2475.1', 'coefficient_field': '1.1.1.1', 'conductor': 2475, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[1, 1, 2], [1], [1], [1, -3, 7], [1, 1], [1, 2, 13], [1, 3, 17], [1, 1, 19], [1, 1, 23], [1, 6, 29], [1, -4, 31], [1, 1, 37], [1, -5, 41], [1, 4, 43], [1, 3, 47], [1, 10, 53], [1, 11, 59], [1, -14, 61], [1, 2, 67], [1, -5, 71], [1, 2, 73], [1, -5, 79], [1, 8, 83], [1, -10, 89], [1, -17, 97], [1, -11, 101], [1, 2, 103], [1, 18, 107], [1, 12, 109], [1, 18, 113]], 'euler_factors_factorization': [[[[1, 1, 2], 1]], [1], [1], [[[1, -3, 7], 1]], [[[1, 1], 1]], [[[1, 2, 13], 1]], [[[1, 3, 17], 1]], [[[1, 1, 19], 1]], [[[1, 1, 23], 1]], [[[1, 6, 29], 1]], [[[1, -4, 31], 1]], [[[1, 1, 37], 1]], [[[1, -5, 41], 1]], [[[1, 4, 43], 1]], [[[1, 3, 47], 1]], [[[1, 10, 53], 1]], [[[1, 11, 59], 1]], [[[1, -14, 61], 1]], [[[1, 2, 67], 1]], [[[1, -5, 71], 1]], [[[1, 2, 73], 1]], [[[1, -5, 79], 1]], [[[1, 8, 83], 1]], [[[1, -10, 89], 1]], [[[1, -17, 97], 1]], [[[1, -11, 101], 1]], [[[1, 2, 103], 1]], [[[1, 18, 107], 1]], [[[1, 12, 109], 1]], [[[1, 18, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 54, 'label': '2-2475-1.1-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/2475/2/a/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-8.441179903270631e-61, 0.11197503780946155, 0.22348838947519004, 0.33404529253476173, 0.44308701260326194, 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3.554811677193894, 2.9980655627435318, 2.36893695534427, 1.698811567857958, 1.0208629941729717, 0.3683863933895257, -0.22688404156675038, -0.7363857478735341], 'positive_zeros': ['1.42734846445239921757802359873634', '2.35667797071707152789075717627409', '3.80888706948583729809072577282532', '4.72076358349491808912876066304458', '5.13569250388043882655281554122863', '6.31018569651781389923413435678738', '7.37326409570226547636119611447903', '7.925108494003391656542258459330918', '8.503195786802655471275015261859974'], 'prelabel': '2-2475-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.445556714323517, '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': 866718538947574653, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.42734846445239921757802359874', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.35667797071707152789075717627', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.80888706948583729809072577283', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.762974500266903, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 2475, 'conductor_radical': 165, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, -1, 0, 0, 3, 3, 0, 0, -1, 0, -2, -3, 0, -1, -3, 0, -1, 0, 0, 1, -1, 0, 0, 2, 0, -3, -6, 0, 4, -5, 0, 3, 0, 0, -1, 1, 0, 0, 5, 0, -4, 1, 0, 1, -3, 0, 2, 0, 0, 2, -10, 0, 0, 9, 0, 6, -11, 0, 14, -4, 0, 7, 0, 0, -2, 3, 0, 0, 5, 0, -2, 1, 0, 1, -3, 0, 5, 0, 0, -5, -8, 0, 0, 4, 0, -3, 10, 0, -6, 1, 0, 3, 0, 0, 17, -2, 0, 0], 'euler11': [1, 1, 0], 'euler13': [1, 2, 13], 'euler17': [1, 3, 17], 'euler19': [1, 1, 19], 'euler2': [1, 1, 2], 'euler23': [1, 1, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, 1, 37], 'euler41': [1, -5, 41], 'euler43': [1, 4, 43], 'euler47': [1, 3, 47], 'euler5': [1, 0, 0], 'euler53': [1, 10, 53], 'euler59': [1, 11, 59], 'euler61': [1, -14, 61], 'euler67': [1, 2, 67], 'euler7': [1, -3, 7], 'euler71': [1, -5, 71], 'euler73': [1, 2, 73], 'euler79': [1, -5, 79], 'euler83': [1, 8, 83], 'euler89': [1, -10, 89], 'euler97': [1, -17, 97], 'euler_factors': [[1, 1, 2], [1, 0, 0], [1, 0, 0], [1, -3, 7], [1, 1, 0], [1, 2, 13], [1, 3, 17], [1, 1, 19], [1, 1, 23], [1, 6, 29], [1, -4, 31], [1, 1, 37], [1, -5, 41], [1, 4, 43], [1, 3, 47], [1, 10, 53], [1, 11, 59], [1, -14, 61], [1, 2, 67], [1, -5, 71], [1, 2, 73], [1, -5, 79], [1, 8, 83], [1, -10, 89], [1, -17, 97]], 'index': 54, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2475/d', 'ModularForm/GL2/Q/holomorphic/2475/2/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/2475/2/a/d'], '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': '2-2475-1.1-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': '2-2475-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.445556714323517, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 866718538947574653, 'z1': {'__RealLiteral__': 0, 'data': '1.42734846445239921757802359874', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20717552
{'Lhash': '1809379137697925425371521585675', 'Lhash_array': ['1809379137697925425371521585675'], 'label': '2-2475-1.1-c1-0-54', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2475/2/a/d'}
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id: 24557383
{'Lhash': '1809379137697925425371521585675', 'Lhash_array': ['1809379137697925425371521585675'], 'label': '2-2475-1.1-c1-0-54', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2475/2/a/d/1/1'}
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id: 30920
{'Lhash': '866718538947574653', 'Lhash_array': ['866718538947574653'], 'label': '2-2475-1.1-c1-0-54', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2475/d'}