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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': -1, 'A8': 0, 'A9': -3, 'Lhash': '1166807296115664074591402165615', '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': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 57.47430058395051, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 1]], [3, [1, 0, 3]], [7, [1, 1]], [73, [1, -17, 89, -73]]], 'bad_primes': [2, 3, 7, 73], 'central_character': '901404.1', 'coefficient_field': '1.1.1.1', 'conductor': 901404, 'conductor_radical': 3066, 'degree': 4, 'euler_factors': [[1, 0, 1], [1, 0, 3], [1, 0, -8, 0, 25], [1, 1], [1, 0, -4, 0, 121], [1, 6, 34, 78, 169], [1, 0, -20, 0, 289], [1, 0, 34, 0, 361], [1, 0, 26, 0, 529], [1, 0, -22, 0, 841], [1, 6, 70, 186, 961], [1, -8, 54, -296, 1369], [1, 0, -62, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, -14, 0, 2209], [1, 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-0.7130984475351532, -1.2956825786215134, -1.776004823874377], 'positive_zeros': ['0.920448659832283933640261317476299', '2.07424052785995222127260664668836', '2.74154791529486118242986057438070', '2.96297744721935200465180770405703', '3.74947567953645638022669054008504', '4.28519418594894667147101211517337', '4.85937608862981009111570410508621', '5.17871363454874673458612847932304', '5.66161128027398707240359691807236', '6.12723577952151804587764415774252', '6.66959596408741876407724833666504', '7.13641414814088792697999514612939', '7.49295013671548862296143041230058', '8.054164276153657025216058182677549'], 'prelabel': '4-901404-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.75339439335373, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1253100797569442755, 'z1': {'__RealLiteral__': 0, 'data': '0.920448659832283933640261317476299', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '2.07424052785995222127260664668836', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.74154791529486118242986057438070', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 57.47430058395051, 'bad_primes': [2, 3, 7, 73], 'central_character': '1.1', 'conductor': 901404, 'conductor_radical': 3066, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -1, 0, 0, -1, 0, -3, 0, 0, 0, -6, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 1, 0, 0, -6, 0, 0, 0, 0, 3, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 1, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 3, -1, 0, 0, 4, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, -2, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, -8], 'euler11': [1, 0, -4, 0, 121], 'euler13': [1, 6, 34, 78, 169], 'euler17': [1, 0, -20, 0, 289], 'euler19': [1, 0, 34, 0, 361], 'euler2': [1, 0, 1, 0, 0], 'euler23': [1, 0, 26, 0, 529], 'euler29': [1, 0, -22, 0, 841], 'euler3': [1, 0, 3, 0, 0], 'euler31': [1, 6, 70, 186, 961], 'euler37': [1, -8, 54, -296, 1369], 'euler41': [1, 0, -62, 0, 1681], 'euler43': [1, -8, 102, -344, 1849], 'euler47': [1, 0, -14, 0, 2209], 'euler5': [1, 0, -8, 0, 25], 'euler53': [1, 0, 38, 0, 2809], 'euler59': [1, 0, -62, 0, 3481], 'euler61': [1, 12, 94, 732, 3721], 'euler67': [1, -4, 102, -268, 4489], 'euler7': [1, 1, 0, 0, 0], 'euler71': [1, 0, 2, 0, 5041], 'euler73': [1, -17, 89, -73, 0], 'euler79': [1, 2, 150, 158, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, 0, 70, 0, 7921], 'euler97': [1, 0, 190, 0, 9409], 'euler_factors': [[1, 0, 1, 0, 0], [1, 0, 3, 0, 0], [1, 0, -8, 0, 25], [1, 1, 0, 0, 0], [1, 0, -4, 0, 121], [1, 6, 34, 78, 169], [1, 0, -20, 0, 289], [1, 0, 34, 0, 361], [1, 0, 26, 0, 529], [1, 0, -22, 0, 841], [1, 6, 70, 186, 961], [1, -8, 54, -296, 1369], [1, 0, -62, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, -14, 0, 2209], [1, 0, 38, 0, 2809], [1, 0, -62, 0, 3481], [1, 12, 94, 732, 3721], [1, -4, 102, -268, 4489], [1, 0, 2, 0, 5041], [1, -17, 89, -73, 0], [1, 2, 150, 158, 6241], [1, 0, 22, 0, 6889], [1, 0, 70, 0, 7921], [1, 0, 190, 0, 9409]], 'index': 4, 'instance_types': ['ECNF', 'ECNF', 'BMF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.3.1/100156.5/c', 'EllipticCurve/2.0.3.1/100156.4/c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/100156.4/c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/100156.5/c'], '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': '4-901404-1.1-c1e2-0-4', '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': 1, 'prelabel': '4-901404-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.75339439335373, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1253100797569442755, 'z1': {'__RealLiteral__': 0, 'data': '0.920448659832283933640261317476299', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9670941
{'Lhash': '1166807296115664074591402165615', 'Lhash_array': ['1166807296115664074591402165615'], 'label': '4-901404-1.1-c1e2-0-4', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/100156.5/c'}
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id: 9670940
{'Lhash': '1166807296115664074591402165615', 'Lhash_array': ['1166807296115664074591402165615'], 'label': '4-901404-1.1-c1e2-0-4', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/100156.4/c'}
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id: 9670877
{'Lhash': '1166807296115664074591402165615', 'Lhash_array': ['1166807296115664074591402165615'], 'label': '4-901404-1.1-c1e2-0-4', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/100156.4/c'}
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id: 9670195
{'Lhash': '1166807296115664074591402165615', 'Lhash_array': ['1166807296115664074591402165615'], 'label': '4-901404-1.1-c1e2-0-4', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/100156.5/c'}