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lfunc_lfunctions • Show schema
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{'Lhash': '1185754483611138494663437825429', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -3, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.348612101957944, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '1296.1', 'coefficient_field': '1.1.1.1', 'conductor': 1296, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1], [1], [1, 3, 5], [1, -4, 7], [1, 0, 11], [1, 1, 13], [1, 3, 17], [1, -4, 19], [1, 0, 23], [1, -9, 29], [1, -4, 31], [1, 1, 37], [1, -6, 41], [1, 8, 43], [1, -12, 47], [1, 6, 53], [1, 0, 59], [1, 1, 61], [1, -4, 67], [1, -12, 71], [1, -11, 73], [1, -16, 79], [1, -12, 83], [1, 3, 89], [1, -2, 97], [1, 6, 101], [1, -4, 103], [1, 12, 107], [1, -11, 109], [1, 15, 113]], 'euler_factors_factorization': [[1], [1], [[[1, 3, 5], 1]], [[[1, -4, 7], 1]], [[[1, 0, 11], 1]], [[[1, 1, 13], 1]], [[[1, 3, 17], 1]], [[[1, -4, 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1.6561882032468371, 1.9378380538010918, 2.110647810736434, 2.1642293645304567, 2.096759703182906, 1.9149525469678668, 1.6334478390355465, 1.2736603774291706, 0.8621658949615678, 0.4287349529112523, 0.00414986394037552, -0.3820442924532235], 'positive_zeros': ['0.935395355311356120178486862504547', '2.41615112845105918353887046447017', '3.68824329939728705086964001390508', '4.60529471992634973001671480526510', '5.10609983558079824652464594115680', '6.50974172394367970294419909175405', '7.44571478799237129140639120121856', '8.047221009677602422962699873620632', '8.542414927665885183690210552564068', '9.598605566629630565849257506422573'], 'prelabel': '2-6e4-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.216925877597733, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1588227601331901313, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.935395355311356120178486862505', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.41615112845105918353887046447', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68824329939728705086964001391', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.348612101957944, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 1296, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -3, 0, 4, 0, 0, 0, 0, 0, -1, 0, 0, 0, -3, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 9, 0, 4, 0, 0, 0, -12, 0, -1, 0, 0, 0, 6, 0, -8, 0, 0, 0, 12, 0, 9, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 3, 0, 4, 0, 0, 0, 12, 0, 11, 0, 0, 0, 0, 0, 16, 0, 0, 0, 12, 0, 9, 0, 0, 0, -3, 0, -4, 0, 0, 0, -12, 0, 2, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 1, 13], 'euler17': [1, 3, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -9, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, 1, 37], 'euler41': [1, -6, 41], 'euler43': [1, 8, 43], 'euler47': [1, -12, 47], 'euler5': [1, 3, 5], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, 1, 61], 'euler67': [1, -4, 67], 'euler7': [1, -4, 7], 'euler71': [1, -12, 71], 'euler73': [1, -11, 73], 'euler79': [1, -16, 79], 'euler83': [1, -12, 83], 'euler89': [1, 3, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 3, 5], [1, -4, 7], [1, 0, 11], [1, 1, 13], [1, 3, 17], [1, -4, 19], [1, 0, 23], [1, -9, 29], [1, -4, 31], [1, 1, 37], [1, -6, 41], [1, 8, 43], [1, -12, 47], [1, 6, 53], [1, 0, 59], [1, 1, 61], [1, -4, 67], [1, -12, 71], [1, -11, 73], [1, -16, 79], [1, -12, 83], [1, 3, 89], [1, -2, 97]], 'index': 3, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1296/c', 'ModularForm/GL2/Q/holomorphic/1296/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/1296/2/a/c'], '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': '2-6e4-1.1-c1-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-6e4-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.216925877597733, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1588227601331901313, 'z1': {'__RealLiteral__': 0, 'data': '0.935395355311356120178486862505', 'prec': 107}}
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lfunc_instances • Show schema
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id: 20739473
{'Lhash': '1185754483611138494663437825429', 'Lhash_array': ['1185754483611138494663437825429'], 'label': '2-6e4-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1296/2/a/c'}
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id: 24552564
{'Lhash': '1185754483611138494663437825429', 'Lhash_array': ['1185754483611138494663437825429'], 'label': '2-6e4-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1296/2/a/c/1/1'}
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id: 41577
{'Lhash': '1588227601331901313', 'Lhash_array': ['1588227601331901313'], 'label': '2-6e4-1.1-c1-0-3', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1296/c'}