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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 4, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '452970271107494187,848164726588554476', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [1.788854381999832, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 99.30780544207177, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, -1]], [13, [1, 2, 1]]], 'bad_primes': [2, 3, 13], 'central_character': '1557504.1', 'coefficient_field': '1.1.1.1', 'conductor': 1557504, 'conductor_radical': 78, 'degree': 4, 'euler_factors': [[1], [1, 0, -1], [1, -4, 14, -20, 25], [1, 0, 10, 0, 49], [1, 0, 18, 0, 121], [1, 2, 1], [1, -12, 70, -204, 289], [1, 0, 34, 0, 361], [1, 0, 46, 0, 529], [1, -4, 62, -116, 841], [1, 0, 58, 0, 961], [1, -20, 174, -740, 1369], [1, -4, 86, -164, 1681], [1, 0, 22, 0, 1849], [1, 0, 90, 0, 2209], [1, 4, 110, 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0.4508919358294746, 0.04335513661282582], 'positive_zeros': ['0.983919193523929230329764658750717', '1.33803744783185283027867448010449', '2.36636166197971073120579022542918', '2.38879148145950189793255761662770', '3.37296560686463484601752098731940', '3.55810218913298118185059814514130', '4.65680782039109928862677817629945', '4.68403548258509043319774249782986', '5.44020310407890724415031834900055', '5.78517701336628451955041513916047', '6.14841639240660146897531624691799', '6.28159176985699903858961238085766', '7.06541986235410893916933421520023', '7.59875356765337238034292890320933', '7.896842730015818559963999252703950'], 'prelabel': '4-1248e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.1567911195161136, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1301134997696048663, 'z1': {'__RealLiteral__': 0, 'data': '0.983919193523929230329764658750717', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '1.33803744783185283027867448010449', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.36636166197971073120579022542918', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 99.30780544207177, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 1557504, 'conductor_radical': 78, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 4, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, -10, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 48, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0], 'euler11': [1, 0, 18, 0, 121], 'euler13': [1, 2, 1, 0, 0], 'euler17': [1, -12, 70, -204, 289], 'euler19': [1, 0, 34, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, -4, 62, -116, 841], 'euler3': [1, 0, -1, 0, 0], 'euler31': [1, 0, 58, 0, 961], 'euler37': [1, -20, 174, -740, 1369], 'euler41': [1, -4, 86, -164, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, 0, 90, 0, 2209], 'euler5': [1, -4, 14, -20, 25], 'euler53': [1, 4, 110, 212, 2809], 'euler59': [1, 0, 18, 0, 3481], 'euler61': [1, -12, 158, -732, 3721], 'euler67': [1, 0, -62, 0, 4489], 'euler7': [1, 0, 10, 0, 49], 'euler71': [1, 0, -54, 0, 5041], 'euler73': [1, 12, 182, 876, 5329], 'euler79': [1, 0, 142, 0, 6241], 'euler83': [1, 0, 130, 0, 6889], 'euler89': [1, -20, 278, -1780, 7921], 'euler97': [1, -20, 294, -1940, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -1, 0, 0], [1, -4, 14, -20, 25], [1, 0, 10, 0, 49], [1, 0, 18, 0, 121], [1, 2, 1, 0, 0], [1, -12, 70, -204, 289], [1, 0, 34, 0, 361], [1, 0, 46, 0, 529], [1, -4, 62, -116, 841], [1, 0, 58, 0, 961], [1, -20, 174, -740, 1369], [1, -4, 86, -164, 1681], [1, 0, 22, 0, 1849], [1, 0, 90, 0, 2209], [1, 4, 110, 212, 2809], [1, 0, 18, 0, 3481], [1, -12, 158, -732, 3721], [1, 0, -62, 0, 4489], [1, 0, -54, 0, 5041], [1, 12, 182, 876, 5329], [1, 0, 142, 0, 6241], [1, 0, 130, 0, 6889], [1, -20, 278, -1780, 7921], [1, -20, 294, -1940, 9409]], 'index': 25, 'instance_types': ['BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/97344.2/e', 'EllipticCurve/2.0.4.1/97344.2/e'], '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': '4-1248e2-1.1-c1e2-0-25', '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': '4-1248e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.1567911195161136, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1301134997696048663, 'z1': {'__RealLiteral__': 0, 'data': '0.983919193523929230329764658750717', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9783111
{'Lhash': '452970271107494187,848164726588554476', 'Lhash_array': ['452970271107494187', '848164726588554476'], 'label': '4-1248e2-1.1-c1e2-0-25', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/97344.2/e'}
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id: 9783046
{'Lhash': '452970271107494187,848164726588554476', 'Lhash_array': ['452970271107494187', '848164726588554476'], 'label': '4-1248e2-1.1-c1e2-0-25', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/97344.2/e'}