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lfunc_lfunctions • Show schema
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{'Lhash': '4577717953087369770602849526790', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': -4, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8943245026383407, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, 1]]], 'bad_primes': [2, 7], 'central_character': '112.1', 'coefficient_field': '1.1.1.1', 'conductor': 112, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[1], [1, 2, 3], [1, 4, 5], [1, 1], [1, 0, 11], [1, 0, 13], [1, 2, 17], [1, -2, 19], [1, 8, 23], [1, -2, 29], [1, 4, 31], [1, 6, 37], [1, 2, 41], [1, 8, 43], [1, -4, 47], [1, 10, 53], [1, 6, 59], [1, -4, 61], [1, -12, 67], [1, 0, 71], [1, 14, 73], [1, -8, 79], [1, 6, 83], [1, -10, 89], [1, 2, 97], [1, -12, 101], [1, -12, 103], [1, -12, 107], [1, -10, 109], [1, -6, 113]], 'euler_factors_factorization': [[1], [[[1, 2, 3], 1]], [[[1, 4, 5], 1]], [[[1, 1], 1]], [[[1, 0, 11], 1]], [[[1, 0, 13], 1]], [[[1, 2, 17], 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-1.974918834242777, -2.0426288158549504, -1.6205325911899207, -0.8307736646202403, 0.11157086970666141, 0.9486957842109615, 1.4412853935937384, 1.4264014807966787, 0.8582664950818276], 'positive_zeros': ['3.61118272831897977078492843407967', '4.88658861407619853654072156509114', '6.34948564084072494191115955003799', '7.48523560915642098619060234168336', '8.605229056688940905430426859413884', '10.27322067133513101779746201703957', '11.32352412905200120139294012796208', '11.89232979768542588412722720710650', '12.66078317424596834200568998415934'], 'prelabel': '2-112-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9456873175835344, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1890724171953078067, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.61118272831897977078492843408', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.88658861407619853654072156509', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.34948564084072494191115955004', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8943245026383407, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 112, 'conductor_radical': 14, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, 0, -4, 0, -1, 0, 1, 0, 0, 0, 0, 0, 8, 0, -2, 0, 2, 0, 2, 0, -8, 0, 11, 0, 4, 0, 2, 0, -4, 0, 0, 0, 4, 0, -6, 0, 0, 0, -2, 0, -8, 0, -4, 0, 4, 0, 1, 0, 4, 0, -10, 0, 0, 0, -4, 0, -6, 0, 4, 0, -1, 0, 0, 0, 12, 0, 16, 0, 0, 0, -14, 0, -22, 0, 0, 0, 8, 0, -11, 0, -6, 0, 8, 0, -4, 0, 10, 0, 0, 0, 8, 0, -8, 0, -2, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 0, 13], 'euler17': [1, 2, 17], 'euler19': [1, -2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, -2, 29], 'euler3': [1, 2, 3], 'euler31': [1, 4, 31], 'euler37': [1, 6, 37], 'euler41': [1, 2, 41], 'euler43': [1, 8, 43], 'euler47': [1, -4, 47], 'euler5': [1, 4, 5], 'euler53': [1, 10, 53], 'euler59': [1, 6, 59], 'euler61': [1, -4, 61], 'euler67': [1, -12, 67], 'euler7': [1, 1, 0], 'euler71': [1, 0, 71], 'euler73': [1, 14, 73], 'euler79': [1, -8, 79], 'euler83': [1, 6, 83], 'euler89': [1, -10, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 2, 3], [1, 4, 5], [1, 1, 0], [1, 0, 11], [1, 0, 13], [1, 2, 17], [1, -2, 19], [1, 8, 23], [1, -2, 29], [1, 4, 31], [1, 6, 37], [1, 2, 41], [1, 8, 43], [1, -4, 47], [1, 10, 53], [1, 6, 59], [1, -4, 61], [1, -12, 67], [1, 0, 71], [1, 14, 73], [1, -8, 79], [1, 6, 83], [1, -10, 89], [1, 2, 97]], 'index': 2, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/112/a', 'ModularForm/GL2/Q/holomorphic/112/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/112/2/a/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-112-1.1-c1-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-112-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9456873175835344, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1890724171953078067, 'z1': {'__RealLiteral__': 0, 'data': '3.61118272831897977078492843408', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9968463
{'Lhash': '4577717953087369770602849526790', 'Lhash_array': ['4577717953087369770602849526790'], 'label': '2-112-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/112/2/a/a'}
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id: 24546848
{'Lhash': '4577717953087369770602849526790', 'Lhash_array': ['4577717953087369770602849526790'], 'label': '2-112-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/112/2/a/a/1/1'}
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id: 22050
{'Lhash': '1890724171953078067', 'Lhash_array': ['1890724171953078067'], 'label': '2-112-1.1-c1-0-2', 'type': 'ECQ', 'url': 'EllipticCurve/Q/112/a'}