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lfunc_lfunctions • Show schema
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{'Lhash': '2036850978575559175723786498345', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 58.76989588766239, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -1]], [23, [1, 1]]], 'bad_primes': [2, 5, 23], 'central_character': '7360.1', 'coefficient_field': '1.1.1.1', 'conductor': 7360, 'conductor_radical': 230, 'degree': 2, 'euler_factors': [[1], [1, -1, 3], [1, -1], [1, -4, 7], [1, 6, 11], [1, -1, 13], [1, 0, 17], [1, -2, 19], [1, 1], [1, 9, 29], [1, 5, 31], [1, 2, 37], [1, 9, 41], [1, 4, 43], [1, -3, 47], [1, -6, 53], [1, 0, 59], [1, 2, 61], [1, 10, 67], [1, -3, 71], [1, 7, 73], [1, -10, 79], [1, 12, 83], [1, 0, 89], [1, -8, 97], [1, -6, 101], [1, -4, 103], [1, 18, 107], [1, 20, 109], [1, -12, 113]], 'euler_factors_factorization': [[1], [[[1, -1, 3], 1]], [[[1, -1], 1]], [[[1, -4, 7], 1]], [[[1, 6, 11], 1]], [[[1, -1, 13], 1]], [[[1, 0, 17], 1]], [[[1, -2, 19], 1]], [[[1, 1], 1]], [[[1, 9, 29], 1]], [[[1, 5, 31], 1]], [[[1, 2, 37], 1]], [[[1, 9, 41], 1]], [[[1, 4, 43], 1]], [[[1, -3, 47], 1]], [[[1, -6, 53], 1]], [[[1, 0, 59], 1]], [[[1, 2, 61], 1]], [[[1, 10, 67], 1]], [[[1, -3, 71], 1]], [[[1, 7, 73], 1]], [[[1, -10, 79], 1]], [[[1, 12, 83], 1]], [[[1, 0, 89], 1]], [[[1, -8, 97], 1]], [[[1, -6, 101], 1]], [[[1, -4, 103], 1]], [[[1, 18, 107], 1]], [[[1, 20, 109], 1]], [[[1, -12, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 168, 'label': '2-7360-1.1-c1-0-168', '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/7360/2/a/v', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.4761429794848353e-60, 0.2551611320793119, 0.5092360423721116, 0.7610912984647062, 1.009502511272355, 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-1.5806851250451854, -1.5139867868416994, -1.3084171975928411, -0.9653910569381701, -0.4935541802496839, 0.09151212238622847, 0.7679650987115062, 1.508720872580563], 'positive_zeros': ['1.60679210675941933437215064052600', '2.20055142142598196485990492937030', '3.00516559526817580896650163720784', '3.85985262759732037691731621189112', '4.97609218646323069806287622768651', '5.36148560534905755340902991964408', '5.87561817950940617908262993537924', '7.16828124806425342744373666231068', '7.70912611688487041136080373899239'], 'prelabel': '2-7360-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.66615261312103, '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': 1379294691047339221, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60679210675941933437215064053', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.20055142142598196485990492937', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.00516559526817580896650163721', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 58.76989588766239, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 7360, 'conductor_radical': 230, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, 4, 0, -2, 0, -6, 0, 1, 0, 1, 0, 0, 0, 2, 0, 4, 0, -1, 0, 1, 0, -5, 0, -9, 0, -5, 0, -6, 0, 4, 0, -2, 0, 1, 0, -9, 0, -4, 0, -2, 0, 3, 0, 9, 0, 0, 0, 6, 0, -6, 0, 2, 0, 0, 0, -2, 0, -8, 0, 1, 0, -10, 0, -1, 0, 3, 0, -7, 0, 1, 0, -24, 0, 10, 0, 1, 0, -12, 0, 0, 0, -9, 0, 0, 0, 4, 0, -5, 0, 2, 0, 8, 0, 12, 0], 'euler11': [1, 6, 11], 'euler13': [1, -1, 13], 'euler17': [1, 0, 17], 'euler19': [1, -2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, 9, 29], 'euler3': [1, -1, 3], 'euler31': [1, 5, 31], 'euler37': [1, 2, 37], 'euler41': [1, 9, 41], 'euler43': [1, 4, 43], 'euler47': [1, -3, 47], 'euler5': [1, -1, 0], 'euler53': [1, -6, 53], 'euler59': [1, 0, 59], 'euler61': [1, 2, 61], 'euler67': [1, 10, 67], 'euler7': [1, -4, 7], 'euler71': [1, -3, 71], 'euler73': [1, 7, 73], 'euler79': [1, -10, 79], 'euler83': [1, 12, 83], 'euler89': [1, 0, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 0, 0], [1, -1, 3], [1, -1, 0], [1, -4, 7], [1, 6, 11], [1, -1, 13], [1, 0, 17], [1, -2, 19], [1, 1, 0], [1, 9, 29], [1, 5, 31], [1, 2, 37], [1, 9, 41], [1, 4, 43], [1, -3, 47], [1, -6, 53], [1, 0, 59], [1, 2, 61], [1, 10, 67], [1, -3, 71], [1, 7, 73], [1, -10, 79], [1, 12, 83], [1, 0, 89], [1, -8, 97]], 'index': 168, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/7360/v', 'ModularForm/GL2/Q/holomorphic/7360/2/a/v/1/1', 'ModularForm/GL2/Q/holomorphic/7360/2/a/v'], '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': '2-7360-1.1-c1-0-168', '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': '2-7360-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.66615261312103, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1379294691047339221, 'z1': {'__RealLiteral__': 0, 'data': '1.60679210675941933437215064053', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21990004
{'Lhash': '2036850978575559175723786498345', 'Lhash_array': ['2036850978575559175723786498345'], 'label': '2-7360-1.1-c1-0-168', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7360/2/a/v'}
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id: 24579361
{'Lhash': '2036850978575559175723786498345', 'Lhash_array': ['2036850978575559175723786498345'], 'label': '2-7360-1.1-c1-0-168', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7360/2/a/v/1/1'}
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id: 30974
{'Lhash': '1379294691047339221', 'Lhash_array': ['1379294691047339221'], 'label': '2-7360-1.1-c1-0-168', 'type': 'ECQ', 'url': 'EllipticCurve/Q/7360/v'}