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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -6, 'Lhash': '1033206834416654150,1591235155908282334', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 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': 6.864048618337643, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [1, 0, -1]], [13, [1, 1]]], 'bad_primes': [7, 13], 'central_character': '107653.1', 'coefficient_field': '1.1.1.1', 'conductor': 107653, 'conductor_radical': 91, 'degree': 4, 'euler_factors': [[1, 0, 0, 0, 4], [1, 0, 6, 0, 9], [1, 0, 1, 0, 25], [1, 0, -1], [1, 0, -14, 0, 121], [1, 1], [1, -8, 50, -136, 289], [1, 0, 13, 0, 361], [1, -6, 55, -138, 529], [1, 10, 83, 290, 841], [1, 0, 53, 0, 961], [1, 0, 58, 0, 1369], [1, 0, 46, 0, 1681], [1, 2, 87, 86, 1849], [1, 0, 45, 0, 2209], [1, 18, 187, 954, 2809], [1, 0, 54, 0, 3481], [1, 20, 222, 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0.7533372306675435], 'positive_zeros': ['1.57613473105511884594471340975637', '2.68417503048537603951806988505092', '3.11744276397134147631028514627569', '3.69113279097650649608530641418649', '4.66814317251753947271974703426383', '5.27883313770925671699270459708873', '5.57652565474586077264622741417532', '6.16699839705098439022921833192818', '6.69002626594602126625681974704932', '7.43563929744309328324545511818401', '7.88305646625584781075065151405911', '8.157183950347712692726002057248012', '8.998346772410808154035420365471643', '9.207834379220788354016903344415764'], 'prelabel': '4-107653-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.6186206910739382, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 318598981111242533, 'z1': {'__RealLiteral__': 0, 'data': '1.57613473105511884594471340975637', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.68417503048537603951806988505092', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.11744276397134147631028514627569', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.864048618337643, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 107653, 'conductor_radical': 91, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -1, 0, 0, -4, 8, 0, 0, 0, 0, 0, 6, 0, -1, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, -18, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -14, 0, 121], 'euler13': [1, 1, 0, 0, 0], 'euler17': [1, -8, 50, -136, 289], 'euler19': [1, 0, 13, 0, 361], 'euler2': [1, 0, 0, 0, 4], 'euler23': [1, -6, 55, -138, 529], 'euler29': [1, 10, 83, 290, 841], 'euler3': [1, 0, 6, 0, 9], 'euler31': [1, 0, 53, 0, 961], 'euler37': [1, 0, 58, 0, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, 2, 87, 86, 1849], 'euler47': [1, 0, 45, 0, 2209], 'euler5': [1, 0, 1, 0, 25], 'euler53': [1, 18, 187, 954, 2809], 'euler59': [1, 0, 54, 0, 3481], 'euler61': [1, 20, 222, 1220, 3721], 'euler67': [1, 0, 98, 0, 4489], 'euler7': [1, 0, -1, 0, 0], 'euler71': [1, 0, 78, 0, 5041], 'euler73': [1, 0, -23, 0, 5329], 'euler79': [1, -6, 167, -474, 6241], 'euler83': [1, 0, -59, 0, 6889], 'euler89': [1, 0, 169, 0, 7921], 'euler97': [1, 0, 145, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 4], [1, 0, 6, 0, 9], [1, 0, 1, 0, 25], [1, 0, -1, 0, 0], [1, 0, -14, 0, 121], [1, 1, 0, 0, 0], [1, -8, 50, -136, 289], [1, 0, 13, 0, 361], [1, -6, 55, -138, 529], [1, 10, 83, 290, 841], [1, 0, 53, 0, 961], [1, 0, 58, 0, 1369], [1, 0, 46, 0, 1681], [1, 2, 87, 86, 1849], [1, 0, 45, 0, 2209], [1, 18, 187, 954, 2809], [1, 0, 54, 0, 3481], [1, 20, 222, 1220, 3721], [1, 0, 98, 0, 4489], [1, 0, 78, 0, 5041], [1, 0, -23, 0, 5329], [1, -6, 167, -474, 6241], [1, 0, -59, 0, 6889], [1, 0, 169, 0, 7921], [1, 0, 145, 0, 9409]], 'index': 1, 'instance_types': ['HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-637.1-a', 'EllipticCurve/2.2.13.1/637.1/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-107653-1.1-c1e2-0-1', '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': '4-107653-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.6186206910739382, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 318598981111242533, 'z1': {'__RealLiteral__': 0, 'data': '1.57613473105511884594471340975637', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9528489
{'Lhash': '1033206834416654150,1591235155908282334', 'Lhash_array': ['1033206834416654150', '1591235155908282334'], 'factors': ['2-1183-1.1-c1-0-45', '2-91-1.1-c1-0-4'], 'label': '4-107653-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.13.1/637.1/a'}
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id: 9528891
{'Lhash': '1033206834416654150,1591235155908282334', 'Lhash_array': ['1033206834416654150', '1591235155908282334'], 'factors': ['2-1183-1.1-c1-0-45', '2-91-1.1-c1-0-4'], 'label': '4-107653-1.1-c1e2-0-1', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-637.1-a'}