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lfunc_lfunctions • Show schema
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{'Lhash': '69628858432594769357859509681,1331535694864418591545399143093', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -14, 'a6': 0, 'a7': -22, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5557.792009410902, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1, -38, 361]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.1', 'coefficient_field': '1.1.1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1], [1], [1, 14, 99, 350, 625], [1, 22, 219, 1078, 2401], [1, -6, 251, -726, 14641], [1, 0, -210, 0, 28561], [1, -34, 867, -9826, 83521], [1, -38, 361], [1, -4, 1062, -2116, 279841], [1, 0, -114, 0, 707281], [1, 0, -1890, 0, 923521], [1, 0, -1170, 0, 1874161], [1, 0, -1794, 0, 2825761], [1, -42, 4139, -77658, 3418801], [1, 10, 4443, 22090, 4879681], [1, 0, -5586, 0, 7890481], [1, 0, -5810, 0, 12117361], [1, -46, 7971, -171166, 13845841], [1, 0, -7410, 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True, 'sign_arg': 0, 'spectral_label': 'c2e2-0', 'trace_hash': 632954682689551094, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.05492748429264239096485275246', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.967490205696825415777589730866', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.05039645358483421031747458107', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5557.792009410902, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -14, 0, -22, 0, 0, 0, 6, 0, 0, 0, 0, 0, 34, 0, 38, 0, 0, 0, 4, 0, 97, 0, 0, 0, 0, 0, 0, 0, 0, 0, 308, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, -10, 0, 265, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 46, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78, 0, 0, 0, -132, 0, 0, 0, 0, 0, -12, 0, -476, 0, 0, 0, 0, 0, 0, 0, 0, 0, -532, 0, 0, 0, 0, 0], 'euler11': [1, -6, 251, -726, 14641], 'euler13': [1, 0, -210, 0, 28561], 'euler17': [1, -34, 867, -9826, 83521], 'euler19': [1, -38, 361, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -4, 1062, -2116, 279841], 'euler29': [1, 0, -114, 0, 707281], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, -1890, 0, 923521], 'euler37': [1, 0, -1170, 0, 1874161], 'euler41': [1, 0, -1794, 0, 2825761], 'euler43': [1, -42, 4139, -77658, 3418801], 'euler47': [1, 10, 4443, 22090, 4879681], 'euler5': [1, 14, 99, 350, 625], 'euler53': [1, 0, -5586, 0, 7890481], 'euler59': [1, 0, -5810, 0, 12117361], 'euler61': [1, -46, 7971, -171166, 13845841], 'euler67': [1, 0, -7410, 0, 20151121], 'euler7': [1, 22, 219, 1078, 2401], 'euler71': [1, 0, -1890, 0, 25411681], 'euler73': [1, -78, 12179, -415662, 28398241], 'euler79': [1, 0, -3234, 0, 38950081], 'euler83': [1, 12, 13814, 82668, 47458321], 'euler89': [1, 0, -1730, 0, 62742241], 'euler97': [1, 0, 9982, 0, 88529281], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 14, 99, 350, 625], [1, 22, 219, 1078, 2401], [1, -6, 251, -726, 14641], [1, 0, -210, 0, 28561], [1, -34, 867, -9826, 83521], [1, -38, 361, 0, 0], [1, -4, 1062, -2116, 279841], [1, 0, -114, 0, 707281], [1, 0, -1890, 0, 923521], [1, 0, -1170, 0, 1874161], [1, 0, -1794, 0, 2825761], [1, -42, 4139, -77658, 3418801], [1, 10, 4443, 22090, 4879681], [1, 0, -5586, 0, 7890481], [1, 0, -5810, 0, 12117361], [1, -46, 7971, -171166, 13845841], [1, 0, -7410, 0, 20151121], [1, 0, -1890, 0, 25411681], [1, -78, 12179, -415662, 28398241], [1, 0, -3234, 0, 38950081], [1, 12, 13814, 82668, 47458321], [1, 0, -1730, 0, 62742241], [1, 0, 9982, 0, 88529281]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/3/o/b'], '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': '4-2736e2-1.1-c2e2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'prelabel': '4-2736e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.634268951623945, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 632954682689551094, 'z1': {'__RealLiteral__': 0, 'data': '0.05492748429264239096485275246', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '69628858432594769357859509681,1331535694864418591545399143093', 'Lhash_array': ['69628858432594769357859509681', '1331535694864418591545399143093'], 'label': '4-2736e2-1.1-c2e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/3/o/b'}