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lfunc_lfunctions • Show schema
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{'Lhash': '1680853503016067502679343891346', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.650678796170963, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '1960.1', 'coefficient_field': '1.1.1.1', 'conductor': 1960, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[1], [1, 2, 3], [1, 1], [1], [1, -4, 11], [1, 2, 13], [1, 0, 17], [1, 2, 19], [1, 4, 23], [1, -10, 29], [1, 4, 31], [1, 2, 37], [1, -12, 41], [1, 4, 43], [1, 4, 47], [1, -2, 53], [1, 10, 59], [1, 6, 61], [1, -4, 67], [1, 12, 71], [1, -4, 73], [1, 4, 79], [1, 14, 83], [1, 8, 89], [1, -8, 97], [1, 14, 101], [1, 20, 103], [1, 4, 107], [1, -10, 109], [1, 18, 113]], 'euler_factors_factorization': [[1], [[[1, 2, 3], 1]], [[[1, 1], 1]], [1], [[[1, -4, 11], 1]], [[[1, 2, 13], 1]], [[[1, 0, 17], 1]], [[[1, 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1.4104205772178795, 1.404153279346951, 1.3016594289900723, 1.0944419856515866, 0.7788529462088033, 0.35653830165856615, -0.16537927714328737, -0.7743977372780976, -1.453016318941148, -2.1793881592244837], 'positive_zeros': ['1.32595961593316370703892657094978', '2.81457574838920705903756418296604', '4.07506500324096665697518707967498', '4.67179696959216786374064647679235', '5.68272740720851408885613690946369', '6.39409529064572332277892048897789', '6.98510787646150277319641738743071', '7.984654042637741729210238361128090', '8.797314786123979806993947256863378'], 'prelabel': '2-1960-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.9560938811118933, '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': 415383861710267852, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.32595961593316370703892657095', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.81457574838920705903756418297', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.07506500324096665697518707967', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.650678796170963, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 1960, 'conductor_radical': 70, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, 0, -1, 0, 0, 0, 1, 0, 4, 0, -2, 0, 2, 0, 0, 0, -2, 0, 0, 0, -4, 0, 1, 0, 4, 0, 10, 0, -4, 0, -8, 0, 0, 0, -2, 0, 4, 0, 12, 0, -4, 0, -1, 0, -4, 0, 0, 0, 0, 0, 2, 0, -4, 0, 4, 0, -10, 0, -6, 0, 0, 0, 2, 0, 4, 0, 8, 0, -12, 0, 4, 0, -2, 0, 0, 0, -4, 0, -11, 0, -14, 0, 0, 0, -20, 0, -8, 0, 0, 0, 8, 0, 2, 0, 8, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, 2, 13], 'euler17': [1, 0, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, -10, 29], 'euler3': [1, 2, 3], 'euler31': [1, 4, 31], 'euler37': [1, 2, 37], 'euler41': [1, -12, 41], 'euler43': [1, 4, 43], 'euler47': [1, 4, 47], 'euler5': [1, 1, 0], 'euler53': [1, -2, 53], 'euler59': [1, 10, 59], 'euler61': [1, 6, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 12, 71], 'euler73': [1, -4, 73], 'euler79': [1, 4, 79], 'euler83': [1, 14, 83], 'euler89': [1, 8, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 0, 0], [1, 2, 3], [1, 1, 0], [1, 0, 0], [1, -4, 11], [1, 2, 13], [1, 0, 17], [1, 2, 19], [1, 4, 23], [1, -10, 29], [1, 4, 31], [1, 2, 37], [1, -12, 41], [1, 4, 43], [1, 4, 47], [1, -2, 53], [1, 10, 59], [1, 6, 61], [1, -4, 67], [1, 12, 71], [1, -4, 73], [1, 4, 79], [1, 14, 83], [1, 8, 89], [1, -8, 97]], 'index': 23, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1960/b', 'ModularForm/GL2/Q/holomorphic/1960/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/1960/2/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': '2-1960-1.1-c1-0-23', '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': '2-1960-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.9560938811118933, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 415383861710267852, 'z1': {'__RealLiteral__': 0, 'data': '1.32595961593316370703892657095', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20609163
{'Lhash': '1680853503016067502679343891346', 'Lhash_array': ['1680853503016067502679343891346'], 'label': '2-1960-1.1-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1960/2/a/b'}
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id: 24555263
{'Lhash': '1680853503016067502679343891346', 'Lhash_array': ['1680853503016067502679343891346'], 'label': '2-1960-1.1-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1960/2/a/b/1/1'}
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id: 28466
{'Lhash': '415383861710267852', 'Lhash_array': ['415383861710267852'], 'label': '2-1960-1.1-c1-0-23', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1960/b'}