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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 3, 'A8': 0, 'A9': -2, 'Lhash': '1060716697103103436085199753532', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896257, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 72.86489866755561, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1, 3]], [31, [1, -4, 26, 31]]], 'bad_primes': [2, 3, 31], 'central_character': '1142784.1', 'coefficient_field': '1.1.1.1', 'conductor': 1142784, 'conductor_radical': 186, 'degree': 4, 'euler_factors': [[1], [1, -1, 3], [1, 0, 7, 0, 25], [1, -3, 16, -21, 49], [1, 0, -21, 0, 121], [1, -5, 32, -65, 169], [1, 0, -14, 0, 289], [1, -7, 50, -133, 361], [1, 0, 7, 0, 529], [1, 0, -16, 0, 841], [1, -4, 26, 31], [1, -9, 88, -333, 1369], [1, 0, -23, 0, 1681], [1, -2, 38, -86, 1849], [1, 0, 46, 0, 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-3.603393708196583, -2.0542562540606637, -0.20002469714585974, 1.7725272031389825, 3.6519821249840843, 5.229903930531576], 'positive_zeros': ['0.836757933859795967155902860057679', '1.56284056022107850365386695135290', '2.15312807742855363333262914237117', '2.89020100760438059253021076951627', '3.33489208676285362956347948894820', '3.84015841320905354650239051908332', '4.40660693366901712230766505898271', '4.84574940770026474475340192314502', '5.52850166800920951682541086700129', '5.81311481108806217063450475161782', '6.11122279755619925536658942099344', '6.84968875481701167403000759645645', '7.27708068995388789561234657196341', '7.88397742060837631683710051395984', '8.071961672527906863140337165001036'], 'prelabel': '4-1142784-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.9216594388205688, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1878757208524262161, 'z1': {'__RealLiteral__': 0, 'data': '0.836757933859795967155902860057679', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '1.56284056022107850365386695135290', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.15312807742855363333262914237117', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 72.86489866755561, 'bad_primes': [2, 3, 31], 'central_character': '1.1', 'conductor': 1142784, 'conductor_radical': 186, 'degree': 4, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 3, 0, -2, 0, 0, 0, 5, 0, 0, 0, 0, 0, 7, 0, 3, 0, 0, 0, -7, 0, -5, 0, 0, 0, 4, 0, 0, 0, 0, 0, 9, 0, 5, 0, 0, 0, 2, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 11, 0, -6, 0, 0, 0, -10, 0, 0, 0, 0, 0, 13, 0, -7, 0, 0, 0, -9, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 0, 4, 0, 0, 0, -2, 0, 0, 0], 'euler11': [1, 0, -21, 0, 121], 'euler13': [1, -5, 32, -65, 169], 'euler17': [1, 0, -14, 0, 289], 'euler19': [1, -7, 50, -133, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 7, 0, 529], 'euler29': [1, 0, -16, 0, 841], 'euler3': [1, -1, 3, 0, 0], 'euler31': [1, -4, 26, 31, 0], 'euler37': [1, -9, 88, -333, 1369], 'euler41': [1, 0, -23, 0, 1681], 'euler43': [1, -2, 38, -86, 1849], 'euler47': [1, 0, 46, 0, 2209], 'euler5': [1, 0, 7, 0, 25], 'euler53': [1, 0, -38, 0, 2809], 'euler59': [1, 0, -6, 0, 3481], 'euler61': [1, -11, 150, -671, 3721], 'euler67': [1, 10, 78, 670, 4489], 'euler7': [1, -3, 16, -21, 49], 'euler71': [1, 0, -68, 0, 5041], 'euler73': [1, -13, 146, -949, 5329], 'euler79': [1, 9, 166, 711, 6241], 'euler83': [1, 0, -157, 0, 6889], 'euler89': [1, 0, 72, 0, 7921], 'euler97': [1, 2, 114, 194, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -1, 3, 0, 0], [1, 0, 7, 0, 25], [1, -3, 16, -21, 49], [1, 0, -21, 0, 121], [1, -5, 32, -65, 169], [1, 0, -14, 0, 289], [1, -7, 50, -133, 361], [1, 0, 7, 0, 529], [1, 0, -16, 0, 841], [1, -4, 26, 31, 0], [1, -9, 88, -333, 1369], [1, 0, -23, 0, 1681], [1, -2, 38, -86, 1849], [1, 0, 46, 0, 2209], [1, 0, -38, 0, 2809], [1, 0, -6, 0, 3481], [1, -11, 150, -671, 3721], [1, 10, 78, 670, 4489], [1, 0, -68, 0, 5041], [1, -13, 146, -949, 5329], [1, 9, 166, 711, 6241], [1, 0, -157, 0, 6889], [1, 0, 72, 0, 7921], [1, 2, 114, 194, 9409]], 'index': 2, 'instance_types': ['BMF', 'ECNF', 'ECNF', 'BMF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/126976.1/g', 'EllipticCurve/2.0.3.1/126976.2/h', 'EllipticCurve/2.0.3.1/126976.1/g', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/126976.2/h'], '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': '4-1142784-1.1-c1e2-0-2', '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': '4-1142784-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.9216594388205688, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1878757208524262161, 'z1': {'__RealLiteral__': 0, 'data': '0.836757933859795967155902860057679', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9703979
{'Lhash': '1060716697103103436085199753532', 'Lhash_array': ['1060716697103103436085199753532'], 'label': '4-1142784-1.1-c1e2-0-2', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/126976.2/h'}
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id: 9703734
{'Lhash': '1060716697103103436085199753532', 'Lhash_array': ['1060716697103103436085199753532'], 'label': '4-1142784-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/126976.1/g'}
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id: 9703686
{'Lhash': '1060716697103103436085199753532', 'Lhash_array': ['1060716697103103436085199753532'], 'label': '4-1142784-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/126976.2/h'}
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id: 9703280
{'Lhash': '1060716697103103436085199753532', 'Lhash_array': ['1060716697103103436085199753532'], 'label': '4-1142784-1.1-c1e2-0-2', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/126976.1/g'}