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lfunc_lfunctions • Show schema
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{'Lhash': '1597943820227873015094160836264', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 56.342443666215466, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '7056.1', 'coefficient_field': '1.1.1.1', 'conductor': 7056, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[1], [1], [1, 0, 5], [1], [1, 0, 11], [1, 5, 13], [1, 0, 17], [1, 1, 19], [1, 0, 23], [1, 0, 29], [1, -11, 31], [1, -11, 37], [1, 0, 41], [1, -13, 43], [1, 0, 47], [1, 0, 53], [1, 0, 59], [1, 14, 61], [1, 5, 67], [1, 0, 71], [1, 17, 73], [1, 17, 79], [1, 0, 83], [1, 0, 89], [1, 14, 97], [1, 0, 101], [1, 13, 103], [1, 0, 107], [1, 19, 109], [1, 0, 113]], 'euler_factors_factorization': [[1], [1], [[[1, 0, 5], 1]], [1], [[[1, 0, 11], 1]], [[[1, 5, 13], 1]], [[[1, 0, 17], 1]], [[[1, 1, 19], 1]], [[[1, 0, 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-0.4230982744020437, -0.7263293900292963, -0.9370018427324175, -1.0464400996567926, -1.0520200948528857, -0.9573073004098291, -0.7718432308962135, -0.5105900490923382], 'positive_zeros': ['1.26055540851728166156733522039245', '2.47752709868336174623609828675448', '2.89472948302706746664620893750280', '4.33631159443367309398800515423649', '4.43289275430421790726586679842481', '5.59746425303006995358444442729701', '6.11112759203424531180371812898117', '6.96827923611881829072103831107140', '7.67306718287486929393594560850550'], 'prelabel': '2-84e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.506160381061377, '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': 699776388372057168, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26055540851728166156733522039', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47752709868336174623609828675', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.89472948302706746664620893750', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 56.342443666215466, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 7056, 'conductor_radical': 42, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -17, 0, 0, 0, 0, 0, -17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 5, 13], 'euler17': [1, 0, 17], 'euler19': [1, 1, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, -11, 31], 'euler37': [1, -11, 37], 'euler41': [1, 0, 41], 'euler43': [1, -13, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 5], 'euler53': [1, 0, 53], 'euler59': [1, 0, 59], 'euler61': [1, 14, 61], 'euler67': [1, 5, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, 17, 73], 'euler79': [1, 17, 79], 'euler83': [1, 0, 83], 'euler89': [1, 0, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 5], [1, 0, 0], [1, 0, 11], [1, 5, 13], [1, 0, 17], [1, 1, 19], [1, 0, 23], [1, 0, 29], [1, -11, 31], [1, -11, 37], [1, 0, 41], [1, -13, 43], [1, 0, 47], [1, 0, 53], [1, 0, 59], [1, 14, 61], [1, 5, 67], [1, 0, 71], [1, 17, 73], [1, 17, 79], [1, 0, 83], [1, 0, 89], [1, 14, 97]], 'index': 72, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/7056/z', 'ModularForm/GL2/Q/holomorphic/7056/2/a/z/1/1', 'ModularForm/GL2/Q/holomorphic/7056/2/a/z'], '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': '2-84e2-1.1-c1-0-72', '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': '2-84e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.506160381061377, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 699776388372057168, 'z1': {'__RealLiteral__': 0, 'data': '1.26055540851728166156733522039', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21891378
{'Lhash': '1597943820227873015094160836264', 'Lhash_array': ['1597943820227873015094160836264'], 'label': '2-84e2-1.1-c1-0-72', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7056/2/a/z'}
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id: 24577918
{'Lhash': '1597943820227873015094160836264', 'Lhash_array': ['1597943820227873015094160836264'], 'label': '2-84e2-1.1-c1-0-72', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7056/2/a/z/1/1'}
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id: 27996
{'Lhash': '699776388372057168', 'Lhash_array': ['699776388372057168'], 'label': '2-84e2-1.1-c1-0-72', 'type': 'ECQ', 'url': 'EllipticCurve/Q/7056/z'}