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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': 0, 'A8': 0, 'A9': 1, 'Lhash': '2520301853028284429556028316234', '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': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.4407151129086025, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]]], 'bad_primes': [2, 3], 'central_character': '6912.1', 'coefficient_field': '1.1.1.1', 'conductor': 6912, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, -1], [1, 0, -2, 0, 25], [1, 0, -2, 0, 49], [1, 0, 22, 0, 121], [1, 0, -26, 0, 169], [1, 0, -2, 0, 289], [1, 8, 54, 152, 361], [1, 0, -2, 0, 529], [1, 0, 46, 0, 841], [1, 0, -50, 0, 961], [1, 0, -26, 0, 1369], [1, 0, 46, 0, 1681], [1, 8, 102, 344, 1849], [1, 0, 46, 0, 2209], [1, 0, 94, 0, 2809], [1, 0, -26, 0, 3481], [1, 0, -74, 0, 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2.237499952714759, 1.473071930201823, 0.4852408950982043], 'positive_zeros': ['1.98816760121008590841728336960644', '3.07613605045775790107350704793808', '4.06909507182561132242704751543855', '4.73962070672136623195764421330429', '5.70890707132874136144996740956037', '6.54477445805309970383121722168189', '7.00058687928287615515234214778853', '7.937719587681307906842453762127053', '8.349444577383232947413827186180296', '8.983018454044175375625782988654346', '9.474688896854884016708639682987485', '10.40150764058967059638147587638794', '10.51465998221254569934018295358574', '11.33576713873450418581555203819173', '11.94553134327863302125688168550920'], 'prelabel': '4-6912-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.8147783599649414, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 2204694058421146497, 'z1': {'__RealLiteral__': 0, 'data': '1.98816760121008590841728336960644', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.07613605045775790107350704793808', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.06909507182561132242704751543855', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.4407151129086025, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 6912, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 0, -26, 0, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -2, 0, 529], 'euler29': [1, 0, 46, 0, 841], 'euler3': [1, -1, 0, 0, 0], 'euler31': [1, 0, -50, 0, 961], 'euler37': [1, 0, -26, 0, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, 0, 46, 0, 2209], 'euler5': [1, 0, -2, 0, 25], 'euler53': [1, 0, 94, 0, 2809], 'euler59': [1, 0, -26, 0, 3481], 'euler61': [1, 0, -74, 0, 3721], 'euler67': [1, 8, 150, 536, 4489], 'euler7': [1, 0, -2, 0, 49], 'euler71': [1, 0, 94, 0, 5041], 'euler73': [1, -4, 150, -292, 5329], 'euler79': [1, 0, -50, 0, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, 0, 142, 0, 7921], 'euler97': [1, -4, 198, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -1, 0, 0, 0], [1, 0, -2, 0, 25], [1, 0, -2, 0, 49], [1, 0, 22, 0, 121], [1, 0, -26, 0, 169], [1, 0, -2, 0, 289], [1, 8, 54, 152, 361], [1, 0, -2, 0, 529], [1, 0, 46, 0, 841], [1, 0, -50, 0, 961], [1, 0, -26, 0, 1369], [1, 0, 46, 0, 1681], [1, 8, 102, 344, 1849], [1, 0, 46, 0, 2209], [1, 0, 94, 0, 2809], [1, 0, -26, 0, 3481], [1, 0, -74, 0, 3721], [1, 8, 150, 536, 4489], [1, 0, 94, 0, 5041], [1, -4, 150, -292, 5329], [1, 0, -50, 0, 6241], [1, 0, 166, 0, 6889], [1, 0, 142, 0, 7921], [1, -4, 198, -388, 9409]], 'index': 3, 'instance_types': ['ECNF', 'ECNF', 'BMF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.8.1/108.2/a', 'EllipticCurve/2.0.8.1/108.3/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/108.3/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/108.2/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': '4-6912-1.1-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': '4-6912-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.8147783599649414, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2204694058421146497, 'z1': {'__RealLiteral__': 0, 'data': '1.98816760121008590841728336960644', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9816087
{'Lhash': '2520301853028284429556028316234', 'Lhash_array': ['2520301853028284429556028316234'], 'label': '4-6912-1.1-c1e2-0-3', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/108.2/a'}
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id: 9815878
{'Lhash': '2520301853028284429556028316234', 'Lhash_array': ['2520301853028284429556028316234'], 'label': '4-6912-1.1-c1e2-0-3', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/108.3/a'}
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id: 9815731
{'Lhash': '2520301853028284429556028316234', 'Lhash_array': ['2520301853028284429556028316234'], 'label': '4-6912-1.1-c1e2-0-3', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/108.3/a'}
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id: 9815523
{'Lhash': '2520301853028284429556028316234', 'Lhash_array': ['2520301853028284429556028316234'], 'label': '4-6912-1.1-c1e2-0-3', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/108.2/a'}