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lfunc_lfunctions • Show schema
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{'Lhash': '1037581529136333597242280713168', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.68190985510838, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -1]], [29, [1, 1]]], 'bad_primes': [2, 3, 5, 29], 'central_character': '5220.1', 'coefficient_field': '1.1.1.1', 'conductor': 5220, 'conductor_radical': 870, 'degree': 2, 'euler_factors': [[1], [1], [1, -1], [1, 0, 7], [1, -2, 11], [1, 2, 13], [1, 0, 17], [1, 2, 19], [1, -8, 23], [1, 1], [1, -2, 31], [1, 4, 37], [1, -10, 41], [1, -4, 43], [1, 12, 47], [1, -6, 53], [1, -12, 59], [1, 10, 61], [1, -12, 67], [1, 12, 71], [1, -12, 73], [1, -2, 79], [1, -4, 83], [1, -10, 89], [1, -8, 97], [1, -6, 101], [1, 0, 103], [1, 4, 107], [1, -6, 109], [1, -4, 113]], 'euler_factors_factorization': [[1], [1], [[[1, -1], 1]], [[[1, 0, 7], 1]], [[[1, -2, 11], 1]], [[[1, 2, 13], 1]], 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1.3277488405482876, 1.7075262369172564, 1.976330834788322, 2.122721731514333, 2.1431003756435056, 2.0419231863179985, 1.8314040110289036, 1.5307221827423867, 1.1647836022104017, 0.7626112397544862, 0.35546582911368924, -0.025184311479093297, -0.349714696852949, -0.5922852448899096], 'positive_zeros': ['0.818507504315089756918734201417635', '1.90973723859044679527840059360478', '2.80202439488109963705600728718797', '3.67639923117339100925767909920261', '4.65076926295003452163252799768408', '5.21459022786390552201057580365092', '6.14396794113848450870733092737548', '6.74495336694957776906239452940698', '7.40033147493330085989839512368576', '8.250401784634935116424626951762969'], 'prelabel': '2-5220-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.4561528680095845, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1754288664458655132, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.818507504315089756918734201418', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.90973723859044679527840059360', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.80202439488109963705600728719', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.68190985510838, 'bad_primes': [2, 3, 5, 29], 'central_character': '1.1', 'conductor': 5220, 'conductor_radical': 870, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 8, 0, 1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 10, 0, 4, 0, 0, 0, -12, 0, -7, 0, 0, 0, 6, 0, 2, 0, 0, 0, 12, 0, -10, 0, 0, 0, -2, 0, 12, 0, 0, 0, -12, 0, 12, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, -2, 0, 8, 0, 0, 0], 'euler11': [1, -2, 11], 'euler13': [1, 2, 13], 'euler17': [1, 0, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, 1, 0], 'euler3': [1, 0, 0], 'euler31': [1, -2, 31], 'euler37': [1, 4, 37], 'euler41': [1, -10, 41], 'euler43': [1, -4, 43], 'euler47': [1, 12, 47], 'euler5': [1, -1, 0], 'euler53': [1, -6, 53], 'euler59': [1, -12, 59], 'euler61': [1, 10, 61], 'euler67': [1, -12, 67], 'euler7': [1, 0, 7], 'euler71': [1, 12, 71], 'euler73': [1, -12, 73], 'euler79': [1, -2, 79], 'euler83': [1, -4, 83], 'euler89': [1, -10, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -1, 0], [1, 0, 7], [1, -2, 11], [1, 2, 13], [1, 0, 17], [1, 2, 19], [1, -8, 23], [1, 1, 0], [1, -2, 31], [1, 4, 37], [1, -10, 41], [1, -4, 43], [1, 12, 47], [1, -6, 53], [1, -12, 59], [1, 10, 61], [1, -12, 67], [1, 12, 71], [1, -12, 73], [1, -2, 79], [1, -4, 83], [1, -10, 89], [1, -8, 97]], 'index': 15, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/5220/n', 'ModularForm/GL2/Q/holomorphic/5220/2/a/n/1/1', 'ModularForm/GL2/Q/holomorphic/5220/2/a/n'], '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': '2-5220-1.1-c1-0-15', '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': '2-5220-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.4561528680095845, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1754288664458655132, 'z1': {'__RealLiteral__': 0, 'data': '0.818507504315089756918734201418', 'prec': 107}}
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lfunc_instances • Show schema
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id: 21320254
{'Lhash': '1037581529136333597242280713168', 'Lhash_array': ['1037581529136333597242280713168'], 'factors': ['2-5220-1.1-c1-0-15'], 'label': '2-5220-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5220/2/a/n'}
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id: 24569459
{'Lhash': '1037581529136333597242280713168', 'Lhash_array': ['1037581529136333597242280713168'], 'factors': ['2-5220-1.1-c1-0-15'], 'label': '2-5220-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5220/2/a/n/1/1'}
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id: 87930
{'Lhash': '1754288664458655132', 'Lhash_array': ['1754288664458655132'], 'factors': ['2-5220-1.1-c1-0-15'], 'label': '2-5220-1.1-c1-0-15', 'type': 'ECQ', 'url': 'EllipticCurve/Q/5220/n'}