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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 2, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1115159505181004833719047804849', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792515, 0], 'a4': [1.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.41721180364871, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 2, 3]], [7, [1, 0, 6, -7]], [61, [1, 9, 51, -61]], [67, [1, -15, 81, -67]]], 'bad_primes': [3, 7, 61, 67], 'central_character': '257481.1', 'coefficient_field': '1.1.1.1', 'conductor': 257481, 'conductor_radical': 85827, 'degree': 4, 'euler_factors': [[1, 0, -2, 0, 4], [1, 2, 3], [1, 0, 1, 0, 25], [1, 0, 6, -7], [1, 0, 13, 0, 121], [1, -4, 21, -52, 169], [1, 0, -2, 0, 289], [1, -13, 78, -247, 361], [1, 0, -26, 0, 529], [1, 0, -2, 0, 841], [1, 8, 78, 248, 961], [1, -4, 78, -148, 1369], [1, 0, 13, 0, 1681], [1, 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1129125223260379406, 'z1': {'__RealLiteral__': 0, 'data': '0.879705736722903077499086320215054', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '1.61223534551344215906297635430528', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.60702096202400834840714577719546', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.41721180364871, 'bad_primes': [3, 7, 61, 67], 'central_character': '1.1', 'conductor': 257481, 'conductor_radical': 85827, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 2, 0, 0, 0, 0, 1, 0, 0, -4, 4, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, -1, 0, 4, 0, 0, 0, -8, 0, 0, 0, 0, 2, 4, 0, -8, 0, 0, 0, 10, 0, 0, 0, 0, 0, -6, 0, 0, 8, 0, 0, 0, 0, -26, 0, 0, 0, -9, 0, 0, -8, 0, 0, 15, 0, 0, 0, 0, 0, 13, 0, 2, 26, 0, 0, -20, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 10, 0, 0, -2], 'euler11': [1, 0, 13, 0, 121], 'euler13': [1, -4, 21, -52, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, -13, 78, -247, 361], 'euler2': [1, 0, -2, 0, 4], 'euler23': [1, 0, -26, 0, 529], 'euler29': [1, 0, -2, 0, 841], 'euler3': [1, 2, 3, 0, 0], 'euler31': [1, 8, 78, 248, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 0, 13, 0, 1681], 'euler43': [1, -10, 75, -430, 1849], 'euler47': [1, 0, -80, 0, 2209], 'euler5': [1, 0, 1, 0, 25], 'euler53': [1, 0, 61, 0, 2809], 'euler59': [1, 0, -50, 0, 3481], 'euler61': [1, 9, 51, -61, 0], 'euler67': [1, -15, 81, -67, 0], 'euler7': [1, 0, 6, -7, 0], 'euler71': [1, 0, 106, 0, 5041], 'euler73': [1, -13, 168, -949, 5329], 'euler79': [1, 20, 258, 1580, 6241], 'euler83': [1, 0, 64, 0, 6889], 'euler89': [1, 0, -83, 0, 7921], 'euler97': [1, -10, 210, -970, 9409], 'euler_factors': [[1, 0, -2, 0, 4], [1, 2, 3, 0, 0], [1, 0, 1, 0, 25], [1, 0, 6, -7, 0], [1, 0, 13, 0, 121], [1, -4, 21, -52, 169], [1, 0, -2, 0, 289], [1, -13, 78, -247, 361], [1, 0, -26, 0, 529], [1, 0, -2, 0, 841], [1, 8, 78, 248, 961], [1, -4, 78, -148, 1369], [1, 0, 13, 0, 1681], [1, -10, 75, -430, 1849], [1, 0, -80, 0, 2209], [1, 0, 61, 0, 2809], [1, 0, -50, 0, 3481], [1, 9, 51, -61, 0], [1, -15, 81, -67, 0], [1, 0, 106, 0, 5041], [1, -13, 168, -949, 5329], [1, 20, 258, 1580, 6241], [1, 0, 64, 0, 6889], [1, 0, -83, 0, 7921], [1, -10, 210, -970, 9409]], 'index': 0, 'instance_types': ['BMF', 'ECNF', 'ECNF', 'BMF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/28609.1/a', 'EllipticCurve/2.0.3.1/28609.8/a', 'EllipticCurve/2.0.3.1/28609.1/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/28609.8/a'], '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': '4-257481-1.1-c1e2-0-0', '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': '4-257481-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.0129122844707426, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1129125223260379406, 'z1': {'__RealLiteral__': 0, 'data': '0.879705736722903077499086320215054', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9750507
{'Lhash': '1115159505181004833719047804849', 'Lhash_array': ['1115159505181004833719047804849'], 'label': '4-257481-1.1-c1e2-0-0', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/28609.8/a'}
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id: 9750505
{'Lhash': '1115159505181004833719047804849', 'Lhash_array': ['1115159505181004833719047804849'], 'label': '4-257481-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/28609.1/a'}
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id: 9750412
{'Lhash': '1115159505181004833719047804849', 'Lhash_array': ['1115159505181004833719047804849'], 'label': '4-257481-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/28609.8/a'}
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id: 9750411
{'Lhash': '1115159505181004833719047804849', 'Lhash_array': ['1115159505181004833719047804849'], 'label': '4-257481-1.1-c1e2-0-0', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/28609.1/a'}