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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 2, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -3, 'Lhash': '583871800482177876,1748683526819109368', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [1.1547005383792515, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.570097149630445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [19, [1, -2, 1]]], 'bad_primes': [2, 19], 'central_character': '369664.1', 'coefficient_field': '1.1.1.1', 'conductor': 369664, 'conductor_radical': 38, 'degree': 4, 'euler_factors': [[1], [1, -2, 7, -6, 9], [1, 0, -6, 0, 25], [1, 0, 5, 0, 49], [1, 4, 26, 44, 121], [1, 0, 25, 0, 169], [1, -6, 43, -102, 289], [1, -2, 1], [1, 0, 45, 0, 529], [1, 0, 33, 0, 841], [1, 0, -2, 0, 961], [1, 0, 70, 0, 1369], [1, 16, 146, 656, 1681], [1, 8, 102, 344, 1849], [1, 0, 30, 0, 2209], [1, 0, 105, 0, 2809], [1, 30, 343, 1770, 3481], 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-4.154487723019965, -5.175654231385401, -5.958979554177112, -6.407341159198262], 'positive_zeros': ['1.49207601742473373563863301754693', '2.31224961625843070084602752548763', '3.01072892067414194047812488684155', '3.27846026315236304587310905813023', '3.57195691104337905967362169036606', '4.86338510531971803230901631456414', '5.01088818916226849614299890352710', '5.50702009116960948045704530045376', '6.17646264461499634926610391599343', '6.52280948162697403172717458152607', '7.41068992206199799917476516664713', '7.65960330166497750263390530877026', '8.199448456904276296960401284969674', '8.264845552131759886230905508727934'], 'prelabel': '4-608e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.203384769597414, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 26712318087593293, 'z1': {'__RealLiteral__': 0, 'data': '1.49207601742473373563863301754693', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.31224961625843070084602752548763', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.01072892067414194047812488684155', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.570097149630445, 'bad_primes': [2, 19], 'central_character': '1.1', 'conductor': 369664, 'conductor_radical': 38, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 0, 0, 0, 0, 0, -3, 0, -4, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 6, 0, -14, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -16, 0, -8, 0, 0, 0, 0, 0, -5, 0, 12, 0, 0, 0, 0, 0, 4, 0, -30, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 18, 0, 12, 0, 0, 0, 0, 0, -4, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 12, 0], 'euler11': [1, 4, 26, 44, 121], 'euler13': [1, 0, 25, 0, 169], 'euler17': [1, -6, 43, -102, 289], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 45, 0, 529], 'euler29': [1, 0, 33, 0, 841], 'euler3': [1, -2, 7, -6, 9], 'euler31': [1, 0, -2, 0, 961], 'euler37': [1, 0, 70, 0, 1369], 'euler41': [1, 16, 146, 656, 1681], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, 0, 30, 0, 2209], 'euler5': [1, 0, -6, 0, 25], 'euler53': [1, 0, 105, 0, 2809], 'euler59': [1, 30, 343, 1770, 3481], 'euler61': [1, 0, 118, 0, 3721], 'euler67': [1, 6, 143, 402, 4489], 'euler7': [1, 0, 5, 0, 49], 'euler71': [1, 0, 138, 0, 5041], 'euler73': [1, -18, 227, -1314, 5329], 'euler79': [1, 0, 58, 0, 6241], 'euler83': [1, -12, 202, -996, 6889], 'euler89': [1, 0, 178, 0, 7921], 'euler97': [1, 4, 198, 388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -2, 7, -6, 9], [1, 0, -6, 0, 25], [1, 0, 5, 0, 49], [1, 4, 26, 44, 121], [1, 0, 25, 0, 169], [1, -6, 43, -102, 289], [1, -2, 1, 0, 0], [1, 0, 45, 0, 529], [1, 0, 33, 0, 841], [1, 0, -2, 0, 961], [1, 0, 70, 0, 1369], [1, 16, 146, 656, 1681], [1, 8, 102, 344, 1849], [1, 0, 30, 0, 2209], [1, 0, 105, 0, 2809], [1, 30, 343, 1770, 3481], [1, 0, 118, 0, 3721], [1, 6, 143, 402, 4489], [1, 0, 138, 0, 5041], [1, -18, 227, -1314, 5329], [1, 0, 58, 0, 6241], [1, -12, 202, -996, 6889], [1, 0, 178, 0, 7921], [1, 4, 198, 388, 9409]], 'index': 13, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.8.1/5776.2/d', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/5776.2/d'], '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': '4-608e2-1.1-c1e2-0-13', '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': '4-608e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.203384769597414, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 26712318087593293, 'z1': {'__RealLiteral__': 0, 'data': '1.49207601742473373563863301754693', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9882111
{'Lhash': '583871800482177876,1748683526819109368', 'Lhash_array': ['583871800482177876', '1748683526819109368'], 'label': '4-608e2-1.1-c1e2-0-13', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/5776.2/d'}
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id: 9882195
{'Lhash': '583871800482177876,1748683526819109368', 'Lhash_array': ['583871800482177876', '1748683526819109368'], 'label': '4-608e2-1.1-c1e2-0-13', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/5776.2/d'}