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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 6, 'Lhash': '1479460878910451234350158191120', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [2.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.633679947214205, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1]], [7, [1, 0, 7]], [11, [1, -1]]], 'bad_primes': [2, 7, 11], 'central_character': '260876.1', 'coefficient_field': '1.1.1.1', 'conductor': 260876, 'conductor_radical': 154, 'degree': 4, 'euler_factors': [[1, 0, -1], [1, 0, -6, 0, 9], [1, 0, -2, 0, 25], [1, 0, 7], [1, -1], [1, 0, -6, 0, 169], [1, 0, 26, 0, 289], [1, 0, -34, 0, 361], [1, -16, 110, -368, 529], [1, 0, 22, 0, 841], [1, 0, 10, 0, 961], [1, 12, 110, 444, 1369], [1, 0, 10, 0, 1681], [1, 0, 70, 0, 1849], [1, 0, -86, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, -86, 0, 3481], [1, 0, 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5.26464034441626, 3.8176330575378916, 2.167359842100243], 'positive_zeros': ['1.16708884817637229457185444327410', '1.58133106765564568625613031282304', '2.57866198506403861623716189695865', '3.34620467406033722077754124678047', '3.71793124530211373357479879031194', '4.60740616023990205481710981392596', '4.95407749784441441983128839476091', '5.29637285243714588581784021659140', '6.33539770631464590838934287145603', '6.66654967118821035672744944634396', '7.03037470409764709156473949623906', '7.32615693509824401196563041856276', '7.85272986534120038415407467631832', '8.494149622254059818080035076185420', '9.057391921212177938213328394363858'], 'prelabel': '4-260876-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.0195150091296186, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1958588656833128228, 'z1': {'__RealLiteral__': 0, 'data': '1.16708884817637229457185444327410', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.58133106765564568625613031282304', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.57866198506403861623716189695865', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.633679947214205, 'bad_primes': [2, 7, 11], 'central_character': '1.1', 'conductor': 260876, 'conductor_radical': 154, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 1, 0, 0, 0, 0, 6, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 16, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -12, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -7, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 6, 2], 'euler11': [1, -1, 0, 0, 0], 'euler13': [1, 0, -6, 0, 169], 'euler17': [1, 0, 26, 0, 289], 'euler19': [1, 0, -34, 0, 361], 'euler2': [1, 0, -1, 0, 0], 'euler23': [1, -16, 110, -368, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 0, -6, 0, 9], 'euler31': [1, 0, 10, 0, 961], 'euler37': [1, 12, 110, 444, 1369], 'euler41': [1, 0, 10, 0, 1681], 'euler43': [1, 0, 70, 0, 1849], 'euler47': [1, 0, -86, 0, 2209], 'euler5': [1, 0, -2, 0, 25], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, 0, -86, 0, 3481], 'euler61': [1, 0, 90, 0, 3721], 'euler67': [1, -8, 150, -536, 4489], 'euler7': [1, 0, 7, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, 74, 0, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 0, 158, 0, 6889], 'euler89': [1, 0, -50, 0, 7921], 'euler97': [1, 0, -66, 0, 9409], 'euler_factors': [[1, 0, -1, 0, 0], [1, 0, -6, 0, 9], [1, 0, -2, 0, 25], [1, 0, 7, 0, 0], [1, -1, 0, 0, 0], [1, 0, -6, 0, 169], [1, 0, 26, 0, 289], [1, 0, -34, 0, 361], [1, -16, 110, -368, 529], [1, 0, 22, 0, 841], [1, 0, 10, 0, 961], [1, 12, 110, 444, 1369], [1, 0, 10, 0, 1681], [1, 0, 70, 0, 1849], [1, 0, -86, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, -86, 0, 3481], [1, 0, 90, 0, 3721], [1, -8, 150, -536, 4489], [1, 0, 142, 0, 5041], [1, 0, 74, 0, 5329], [1, 0, 158, 0, 6241], [1, 0, 158, 0, 6889], [1, 0, -50, 0, 7921], [1, 0, -66, 0, 9409]], 'index': 3, 'instance_types': ['ECNF', 'BMF', 'ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.7.1/5324.7/d', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/5324.7/d', 'EllipticCurve/2.0.7.1/5324.6/e', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/5324.6/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': '4-260876-1.1-c1e2-0-3', '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': '4-260876-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.0195150091296186, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1958588656833128228, 'z1': {'__RealLiteral__': 0, 'data': '1.16708884817637229457185444327410', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9642448
{'Lhash': '1479460878910451234350158191120', 'Lhash_array': ['1479460878910451234350158191120'], 'label': '4-260876-1.1-c1e2-0-3', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/5324.6/e'}
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id: 9642311
{'Lhash': '1479460878910451234350158191120', 'Lhash_array': ['1479460878910451234350158191120'], 'label': '4-260876-1.1-c1e2-0-3', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/5324.6/e'}
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id: 9642120
{'Lhash': '1479460878910451234350158191120', 'Lhash_array': ['1479460878910451234350158191120'], 'label': '4-260876-1.1-c1e2-0-3', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/5324.7/d'}
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id: 9641816
{'Lhash': '1479460878910451234350158191120', 'Lhash_array': ['1479460878910451234350158191120'], 'label': '4-260876-1.1-c1e2-0-3', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/5324.7/d'}