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lfunc_lfunctions • Show schema
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{'Lhash': '1756941718896719141192788771858,3584182729031643361641401759912', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.3102346112010315, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -2, 1]], [13, [1, -2, 13]]], 'bad_primes': [2, 5, 13], 'central_character': '260.1', 'coefficient_field': '1.1.1.1', 'conductor': 67600, 'conductor_radical': 130, 'degree': 4, 'euler_factors': [[1], [1, -3, 6, -9, 9], [1, -2, 1], [1, 3, 2, 21, 49], [1, 3, -2, 33, 121], [1, -2, 13], [1, -7, 32, -119, 289], [1, 1, -18, 19, 361], [1, -7, 26, -161, 529], [1, -5, -4, -145, 841], [1, 8, 78, 248, 961], [1, -3, -28, -111, 1369], [1, 7, 8, 287, 1681], [1, -9, 38, -387, 1849], [1, -16, 158, -752, 2209], [1, 12, 142, 636, 2809], [1, 5, -34, 295, 3481], [1, -5, -36, -305, 3721], [1, 13, 102, 871, 4489], [1, -3, -62, -213, 5041], [1, 28, 342, 2044, 5329], 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'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 43027826009262922, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38598263478942632454871572922', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.68229165966164450814091997592', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.82742163210141865177049829200', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.3102346112010315, 'bad_primes': [2, 5, 13], 'central_character': '1.1', 'conductor': 67600, 'conductor_radical': 130, 'degree': 4, 'dirichlet_coefficients': [1, 0, 3, 0, 2, 0, -3, 0, 3, 0, -3, 0, 2, 0, 6, 0, 7, 0, -1, 0, -9, 0, 7, 0, 3, 0, 0, 0, 5, 0, -8, 0, -9, 0, -6, 0, 3, 0, 6, 0, -7, 0, 9, 0, 6, 0, 16, 0, 7, 0, 21, 0, -12, 0, -6, 0, -3, 0, -5, 0, 5, 0, -9, 0, 4, 0, -13, 0, 21, 0, 3, 0, -28, 0, 9, 0, 9, 0, -16, 0, 0, 0, 24, 0, 14, 0, 15, 0, -7, 0, -6, 0, -24, 0, -2, 0, 11, 0, -9, 0], 'euler11': [1, 3, -2, 33, 121], 'euler13': [1, -2, 13, 0, 0], 'euler17': [1, -7, 32, -119, 289], 'euler19': [1, 1, -18, 19, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -7, 26, -161, 529], 'euler29': [1, -5, -4, -145, 841], 'euler3': [1, -3, 6, -9, 9], 'euler31': [1, 8, 78, 248, 961], 'euler37': [1, -3, -28, -111, 1369], 'euler41': [1, 7, 8, 287, 1681], 'euler43': [1, -9, 38, -387, 1849], 'euler47': [1, -16, 158, -752, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, 5, -34, 295, 3481], 'euler61': [1, -5, -36, -305, 3721], 'euler67': [1, 13, 102, 871, 4489], 'euler7': [1, 3, 2, 21, 49], 'euler71': [1, -3, -62, -213, 5041], 'euler73': [1, 28, 342, 2044, 5329], 'euler79': [1, 16, 222, 1264, 6241], 'euler83': [1, -24, 310, -1992, 6889], 'euler89': [1, 7, -40, 623, 7921], 'euler97': [1, -11, 24, -1067, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -3, 6, -9, 9], [1, -2, 1, 0, 0], [1, 3, 2, 21, 49], [1, 3, -2, 33, 121], [1, -2, 13, 0, 0], [1, -7, 32, -119, 289], [1, 1, -18, 19, 361], [1, -7, 26, -161, 529], [1, -5, -4, -145, 841], [1, 8, 78, 248, 961], [1, -3, -28, -111, 1369], [1, 7, 8, 287, 1681], [1, -9, 38, -387, 1849], [1, -16, 158, -752, 2209], [1, 12, 142, 636, 2809], [1, 5, -34, 295, 3481], [1, -5, -36, -305, 3721], [1, 13, 102, 871, 4489], [1, -3, -62, -213, 5041], [1, 28, 342, 2044, 5329], [1, 16, 222, 1264, 6241], [1, -24, 310, -1992, 6889], [1, 7, -40, 623, 7921], [1, -11, 24, -1067, 9409]], 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/260/2/i/d'], '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': '4-260e2-1.1-c1e2-0-11', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-260e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 43027826009262922, 'z1': {'__RealLiteral__': 0, 'data': '1.38598263478942632454871572922', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1756941718896719141192788771858,3584182729031643361641401759912', 'Lhash_array': ['1756941718896719141192788771858', '3584182729031643361641401759912'], 'label': '4-260e2-1.1-c1e2-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/i/d'}