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lfunc_lfunctions • Show schema
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{'A10': -2, 'A2': -1, 'A3': -1, 'A4': -1, 'A5': 2, 'A6': 1, 'A7': 4, 'A8': 3, 'A9': -2, 'Lhash': '894070845311489704280825028388', 'a10': [-0.632455532033676, 0], 'a2': [-0.7071067811865476, 0], 'a3': [-0.5773502691896257, 0], 'a4': [-0.5, 0], 'a5': [0.894427190999916, 0], 'a6': [0.40824829046386296, 0], 'a7': [1.5118578920369088, 0], 'a8': [1.0606601717798214, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 34.38802089334068, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1, 2]], [3, [1, 1, 3, 3]], [53, [1, -6, 53]]], 'bad_primes': [2, 3, 53], 'central_character': '539328.1', 'coefficient_field': '1.1.1.1', 'conductor': 539328, 'conductor_radical': 318, 'degree': 4, 'euler_factors': [[1, 1, 2], [1, 1, 3, 3], [1, -2, 7, -10, 25], [1, -4, 14, -28, 49], [1, 0, 13, 0, 121], [1, 0, -10, 0, 169], [1, -2, 31, -34, 289], [1, -4, 6, -76, 361], [1, 0, -35, 0, 529], [1, 0, 38, 0, 841], [1, 0, 41, 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-2.2856776387141187, -0.5994288326112178, 1.0157964691846275, 2.334633816922551, 3.188918552571494, 3.4910792337494323, 3.2439239227938494, 2.5354681667221155, 1.5199957197761955, 0.38887595766412086, -0.6636225362713505], 'positive_zeros': ['0.70529753636413698670543663922410', '1.57529317101823182442787469255094', '1.98644552801823077734916819016167', '2.92122792171412648845382441658109', '3.63644220835827721308280057347192', '4.44447133404808793949844223755230', '4.72515894793674202931866028576866', '5.41798539240380860950126931939492', '5.55352926625868574311342302718026', '5.99190753089947206603605134234938', '6.65286287723150000318259691782282', '7.43789373245577066589238154656667', '7.58931156546967098088495922730412', '8.048860814486580245989620714867006', '8.553900202097024101892916437176309'], 'prelabel': '4-539328-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.4215965849331536, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 773374511920015137, 'z1': {'__RealLiteral__': 0, 'data': '0.70529753636413698670543663922410', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.57529317101823182442787469255094', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '1.98644552801823077734916819016167', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 34.38802089334068, 'bad_primes': [2, 3, 53], 'central_character': '1.1', 'conductor': 539328, 'conductor_radical': 318, 'degree': 4, 'dirichlet_coefficients': [1, -1, -1, -1, 2, 1, 4, 3, -2, -2, 0, 1, 0, -4, -2, -1, 2, 2, 4, -2, -4, 0, 0, -3, -3, 0, 2, -4, 0, 2, 0, -5, 0, -2, 8, 2, 0, -4, 0, 6, 0, 4, 0, 0, -4, 0, 4, 1, 2, 3, -2, 0, 6, -2, 0, 12, -4, 0, 0, 2, -4, 0, -8, 7, 0, 0, -12, -2, 0, -8, 0, -6, 0, 0, 3, -4, 0, 0, 0, -2, 7, 0, -8, 4, 4, 0, 0, 0, -6, 4, 0, 0, 0, -4, 8, 5, 6, -2, 0, 3], 'euler11': [1, 0, 13, 0, 121], 'euler13': [1, 0, -10, 0, 169], 'euler17': [1, -2, 31, -34, 289], 'euler19': [1, -4, 6, -76, 361], 'euler2': [1, 1, 2, 0, 0], 'euler23': [1, 0, -35, 0, 529], 'euler29': [1, 0, 38, 0, 841], 'euler3': [1, 1, 3, 3, 0], 'euler31': [1, 0, 41, 0, 961], 'euler37': [1, 0, -10, 0, 1369], 'euler41': [1, 0, -18, 0, 1681], 'euler43': [1, 0, 49, 0, 1849], 'euler47': [1, -4, 94, -188, 2209], 'euler5': [1, -2, 7, -10, 25], 'euler53': [1, -6, 53, 0, 0], 'euler59': [1, 0, -67, 0, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 12, 134, 804, 4489], 'euler7': [1, -4, 14, -28, 49], 'euler71': [1, 0, 110, 0, 5041], 'euler73': [1, 0, -34, 0, 5329], 'euler79': [1, 0, -103, 0, 6241], 'euler83': [1, 8, 118, 664, 6889], 'euler89': [1, 6, 183, 534, 7921], 'euler97': [1, -6, 187, -582, 9409], 'euler_factors': [[1, 1, 2, 0, 0], [1, 1, 3, 3, 0], [1, -2, 7, -10, 25], [1, -4, 14, -28, 49], [1, 0, 13, 0, 121], [1, 0, -10, 0, 169], [1, -2, 31, -34, 289], [1, -4, 6, -76, 361], [1, 0, -35, 0, 529], [1, 0, 38, 0, 841], [1, 0, 41, 0, 961], [1, 0, -10, 0, 1369], [1, 0, -18, 0, 1681], [1, 0, 49, 0, 1849], [1, -4, 94, -188, 2209], [1, -6, 53, 0, 0], [1, 0, -67, 0, 3481], [1, 4, 126, 244, 3721], [1, 12, 134, 804, 4489], [1, 0, 110, 0, 5041], [1, 0, -34, 0, 5329], [1, 0, -103, 0, 6241], [1, 8, 118, 664, 6889], [1, 6, 183, 534, 7921], [1, -6, 187, -582, 9409]], 'index': 1, 'instance_types': ['ECNF', 'ECNF', 'HMF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.424.1/3.2/c', 'EllipticCurve/2.2.424.1/3.1/c', 'ModularForm/GL2/TotallyReal/2.2.424.1/holomorphic/2.2.424.1-3.2-c', 'ModularForm/GL2/TotallyReal/2.2.424.1/holomorphic/2.2.424.1-3.1-c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, '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': '4-539328-1.1-c1e2-0-1', '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': '4-539328-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.4215965849331536, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 773374511920015137, 'z1': {'__RealLiteral__': 0, 'data': '0.70529753636413698670543663922410', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9463012
{'Lhash': '894070845311489704280825028388', 'Lhash_array': ['894070845311489704280825028388'], 'label': '4-539328-1.1-c1e2-0-1', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.424.1/holomorphic/2.2.424.1-3.1-c'}
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id: 9463011
{'Lhash': '894070845311489704280825028388', 'Lhash_array': ['894070845311489704280825028388'], 'label': '4-539328-1.1-c1e2-0-1', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.424.1/holomorphic/2.2.424.1-3.2-c'}
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id: 9463007
{'Lhash': '894070845311489704280825028388', 'Lhash_array': ['894070845311489704280825028388'], 'label': '4-539328-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.424.1/3.1/c'}
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id: 9463003
{'Lhash': '894070845311489704280825028388', 'Lhash_array': ['894070845311489704280825028388'], 'label': '4-539328-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.424.1/3.2/c'}