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lfunc_lfunctions • Show schema
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{'Lhash': '1766315353300368017974828056819', 'a10': 0, 'a2': -1, 'a3': -1, 'a4': 1, 'a5': 0, 'a6': 1, 'a7': 1, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.29559707780934, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [19, [1]]], 'bad_primes': [2, 3, 19], 'central_character': '2166.1', 'coefficient_field': '1.1.1.1', 'conductor': 2166, 'conductor_radical': 114, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1, 0, 5], [1, -1, 7], [1, 2, 11], [1, 3, 13], [1, -4, 17], [1], [1, -4, 23], [1, 0, 29], [1, 3, 31], [1, 5, 37], [1, -4, 41], [1, 9, 43], [1, -10, 47], [1, 4, 53], [1, 14, 59], [1, -11, 61], [1, -3, 67], [1, -14, 71], [1, 11, 73], [1, -1, 79], [1, -8, 83], [1, 14, 89], [1, -2, 97], [1, 10, 101], [1, 3, 103], [1, 10, 107], [1, -14, 109], [1, -10, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, 1], 1]], [[[1, 0, 5], 1]], [[[1, -1, 7], 1]], [[[1, 2, 11], 1]], [[[1, 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1.0359326073877233, 0.831198228010577, 0.49794953707596246, 0.04345829369517085, -0.5183895390426098, -1.1675337030115127, -1.878508697640336, -2.6215118556213417, -3.363724106622295, -4.070822900152779], 'positive_zeros': ['1.39337712851029959665204865718984', '2.51427483814275976737711905632584', '3.65234867945545672064962587093903', '4.93280174672246383994875626397681', '5.46004427620403419851851792377819', '6.42341778864721631502457891600037', '7.36673908327557404759318806581248', '7.77595253275059112499995975916905', '8.675868023200687745690978624523970'], 'prelabel': '2-2166-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.158797551914416, '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': 1579928584603254391, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39337712851029959665204865719', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.51427483814275976737711905633', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65234867945545672064962587094', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.29559707780934, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 2166, 'conductor_radical': 114, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 0, 1, 1, -1, 1, 0, -2, -1, -3, -1, 0, 1, 4, -1, 0, 0, -1, 2, 4, 1, -5, 3, -1, 1, 0, 0, -3, -1, 2, -4, 0, 1, -5, 0, 3, 0, 4, 1, -9, -2, 0, -4, 10, -1, -6, 5, -4, -3, -4, 1, 0, -1, 0, 0, -14, 0, 11, 3, 1, 1, 0, -2, 3, 4, -4, 0, 14, -1, -11, 5, 5, 0, -2, -3, 1, 0, 1, -4, 8, -1, 0, 9, 0, 2, -14, 0, -3, 4, 3, -10, 0, 1, 2, 6, -2, -5], 'euler11': [1, 2, 11], 'euler13': [1, 3, 13], 'euler17': [1, -4, 17], 'euler19': [1, 0, 0], 'euler2': [1, 1, 0], 'euler23': [1, -4, 23], 'euler29': [1, 0, 29], 'euler3': [1, 1, 0], 'euler31': [1, 3, 31], 'euler37': [1, 5, 37], 'euler41': [1, -4, 41], 'euler43': [1, 9, 43], 'euler47': [1, -10, 47], 'euler5': [1, 0, 5], 'euler53': [1, 4, 53], 'euler59': [1, 14, 59], 'euler61': [1, -11, 61], 'euler67': [1, -3, 67], 'euler7': [1, -1, 7], 'euler71': [1, -14, 71], 'euler73': [1, 11, 73], 'euler79': [1, -1, 79], 'euler83': [1, -8, 83], 'euler89': [1, 14, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 0, 5], [1, -1, 7], [1, 2, 11], [1, 3, 13], [1, -4, 17], [1, 0, 0], [1, -4, 23], [1, 0, 29], [1, 3, 31], [1, 5, 37], [1, -4, 41], [1, 9, 43], [1, -10, 47], [1, 4, 53], [1, 14, 59], [1, -11, 61], [1, -3, 67], [1, -14, 71], [1, 11, 73], [1, -1, 79], [1, -8, 83], [1, 14, 89], [1, -2, 97]], 'index': 35, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2166/b', 'ModularForm/GL2/Q/holomorphic/2166/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/2166/2/a/b'], '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': '2-2166-1.1-c1-0-35', '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': '2-2166-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.158797551914416, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1579928584603254391, 'z1': {'__RealLiteral__': 0, 'data': '1.39337712851029959665204865719', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20599286
{'Lhash': '1766315353300368017974828056819', 'Lhash_array': ['1766315353300368017974828056819'], 'label': '2-2166-1.1-c1-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2166/2/a/b'}
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id: 24556092
{'Lhash': '1766315353300368017974828056819', 'Lhash_array': ['1766315353300368017974828056819'], 'label': '2-2166-1.1-c1-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2166/2/a/b/1/1'}
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id: 91789
{'Lhash': '1579928584603254391', 'Lhash_array': ['1579928584603254391'], 'label': '2-2166-1.1-c1-0-35', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2166/b'}