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lfunc_lfunctions • Show schema
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{'A10': -2, 'A2': 1, 'A3': 0, 'A4': -1, 'A5': -2, 'A6': 0, 'A7': 0, 'A8': -3, 'A9': 1, 'Lhash': '423591494900522709,1481482587619896808', 'a10': [-0.632455532033676, 0], 'a2': [0.7071067811865476, 0], 'a3': [0.0, 0], 'a4': [-0.5, 0], 'a5': [-0.894427190999916, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [-1.0606601717798214, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 82.86362279166953, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 2]], [3, [1, 0, -1]], [5, [1, 2, 1]], [19, [1, 0, -1]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '1299600.1', 'coefficient_field': '1.1.1.1', 'conductor': 1299600, 'conductor_radical': 570, 'degree': 4, 'euler_factors': [[1, -1, 2], [1, 0, -1], [1, 2, 1], [1, 0, 10, 0, 49], [1, 0, 18, 0, 121], [1, 8, 42, 104, 169], [1, -4, 38, -68, 289], [1, 0, -1], [1, 0, 30, 0, 529], [1, -8, 74, -232, 841], [1, 0, 62, 0, 961], [1, 0, 74, 0, 1369], [1, 0, 82, 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'trace_hash': 1905074082520419517, 'z1': {'__RealLiteral__': 0, 'data': '0.895818257201027131012503394679240', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '1.97779909070487265858566219386783', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.93269055521134332794719136670457', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 82.86362279166953, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 1299600, 'conductor_radical': 570, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, -1, -2, 0, 0, -3, 1, -2, 0, 0, -8, 0, 0, -1, 4, 1, 0, 2, 0, 0, 0, 0, 3, -8, 0, 0, 8, 0, 0, 5, 0, 4, 0, -1, 0, 0, 0, 6, 0, 0, 0, 0, -2, 0, 0, 0, -10, 3, 0, 8, -4, 0, 0, 0, 0, 8, 0, 0, 4, 0, 0, 7, 16, 0, 0, -4, 0, 0, 0, -3, -4, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, -8, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -32, -10, 0, -3], 'euler11': [1, 0, 18, 0, 121], 'euler13': [1, 8, 42, 104, 169], 'euler17': [1, -4, 38, -68, 289], 'euler19': [1, 0, -1, 0, 0], 'euler2': [1, -1, 2, 0, 0], 'euler23': [1, 0, 30, 0, 529], 'euler29': [1, -8, 74, -232, 841], 'euler3': [1, 0, -1, 0, 0], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, 0, 74, 0, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, 0, -14, 0, 1849], 'euler47': [1, 0, -50, 0, 2209], 'euler5': [1, 2, 1, 0, 0], 'euler53': [1, 4, 110, 212, 2809], 'euler59': [1, 0, 102, 0, 3481], 'euler61': [1, -4, 126, -244, 3721], 'euler67': [1, 0, -122, 0, 4489], 'euler7': [1, 0, 10, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 4, 150, 292, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, 0, 178, 0, 7921], 'euler97': [1, 32, 450, 3104, 9409], 'euler_factors': [[1, -1, 2, 0, 0], [1, 0, -1, 0, 0], [1, 2, 1, 0, 0], [1, 0, 10, 0, 49], [1, 0, 18, 0, 121], [1, 8, 42, 104, 169], [1, -4, 38, -68, 289], [1, 0, -1, 0, 0], [1, 0, 30, 0, 529], [1, -8, 74, -232, 841], [1, 0, 62, 0, 961], [1, 0, 74, 0, 1369], [1, 0, 82, 0, 1681], [1, 0, -14, 0, 1849], [1, 0, -50, 0, 2209], [1, 4, 110, 212, 2809], [1, 0, 102, 0, 3481], [1, -4, 126, -244, 3721], [1, 0, -122, 0, 4489], [1, 0, 142, 0, 5041], [1, 4, 150, 292, 5329], [1, 0, 94, 0, 6241], [1, 0, 22, 0, 6889], [1, 0, 178, 0, 7921], [1, 32, 450, 3104, 9409]], 'index': 13, 'instance_types': ['BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/81225.2/b', 'EllipticCurve/2.0.4.1/81225.2/b'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-1140e2-1.1-c1e2-0-13', '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': 1, 'prelabel': '4-1140e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.0171088529295673, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1905074082520419517, 'z1': {'__RealLiteral__': 0, 'data': '0.895818257201027131012503394679240', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9753189
{'Lhash': '423591494900522709,1481482587619896808', 'Lhash_array': ['423591494900522709', '1481482587619896808'], 'label': '4-1140e2-1.1-c1e2-0-13', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/81225.2/b'}
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id: 9754131
{'Lhash': '423591494900522709,1481482587619896808', 'Lhash_array': ['423591494900522709', '1481482587619896808'], 'label': '4-1140e2-1.1-c1e2-0-13', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/81225.2/b'}