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lfunc_lfunctions • Show schema
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{'Lhash': '1968917635246237463472152954170,2732795437665816571465905772540', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 4, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.2278938933735533, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '225.1', 'coefficient_field': '1.1.1.1', 'conductor': 50625, 'conductor_radical': 15, 'degree': 4, 'euler_factors': [[1, 0, -4, 0, 4], [1], [1], [1, 0, 11, 0, 49], [1, 0, 22, 0, 121], [1, 0, -1, 0, 169], [1, 0, -34, 0, 289], [1, -2, 39, -38, 361], [1, 0, -46, 0, 529], [1, 0, 58, 0, 841], [1, 14, 111, 434, 961], [1, 0, 26, 0, 1369], [1, 0, 82, 0, 1681], [1, 0, -61, 0, 1849], [1, 0, -94, 0, 2209], [1, 0, -106, 0, 2809], [1, 0, 118, 0, 3481], [1, 26, 291, 1586, 3721], [1, 0, -109, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, -46, 0, 5329], [1, -8, 174, -632, 6241], [1, 0, -166, 0, 6889], [1, 0, 178, 0, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.2278938933735533, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 50625, 'conductor_radical': 15, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 0, -1, 0, 169], 'euler17': [1, 0, -34, 0, 289], 'euler19': [1, -2, 39, -38, 361], 'euler2': [1, 0, -4, 0, 4], 'euler23': [1, 0, -46, 0, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 14, 111, 434, 961], 'euler37': [1, 0, 26, 0, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, 0, -61, 0, 1849], 'euler47': [1, 0, -94, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -106, 0, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, 26, 291, 1586, 3721], 'euler67': [1, 0, -109, 0, 4489], 'euler7': [1, 0, 11, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, -46, 0, 5329], 'euler79': [1, -8, 174, -632, 6241], 'euler83': [1, 0, -166, 0, 6889], 'euler89': [1, 0, 178, 0, 7921], 'euler97': [1, 0, -169, 0, 9409], 'euler_factors': [[1, 0, -4, 0, 4], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 11, 0, 49], [1, 0, 22, 0, 121], [1, 0, -1, 0, 169], [1, 0, -34, 0, 289], [1, -2, 39, -38, 361], [1, 0, -46, 0, 529], [1, 0, 58, 0, 841], [1, 14, 111, 434, 961], [1, 0, 26, 0, 1369], [1, 0, 82, 0, 1681], [1, 0, -61, 0, 1849], [1, 0, -94, 0, 2209], [1, 0, -106, 0, 2809], [1, 0, 118, 0, 3481], [1, 26, 291, 1586, 3721], [1, 0, -109, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, -46, 0, 5329], [1, -8, 174, -632, 6241], [1, 0, -166, 0, 6889], [1, 0, 178, 0, 7921], [1, 0, -169, 0, 9409]], 'index': 5, 'instance_types': ['ECNF', 'HMF', 'CMF'], 'instance_urls': ['EllipticCurve/2.2.5.1/2025.1/c', 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-2025.1-c', 'ModularForm/GL2/Q/holomorphic/225/2/b/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-15e4-1.1-c1e2-0-5', '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': '4-15e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 551082004981334597, 'z1': {'__RealLiteral__': 0, 'data': '1.55320214804596082455230921611', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10064097
{'Lhash': '1968917635246237463472152954170,2732795437665816571465905772540', 'Lhash_array': ['1968917635246237463472152954170', '2732795437665816571465905772540'], 'label': '4-15e4-1.1-c1e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/b/c'}
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id: 9517268
{'Lhash': '_1968917635246237463472152954170', 'Lhash_array': ['_1968917635246237463472152954170'], 'label': '4-15e4-1.1-c1e2-0-5', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-2025.1-c'}
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id: 9517006
{'Lhash': '_1968917635246237463472152954170', 'Lhash_array': ['_1968917635246237463472152954170'], 'label': '4-15e4-1.1-c1e2-0-5', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.5.1/2025.1/c'}