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lfunc_lfunctions • Show schema
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{'Lhash': '2638940703258648350892128998475', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.179056282979259, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1, -1]]], 'bad_primes': [2, 5, 7], 'central_character': '1400.1', 'coefficient_field': '1.1.1.1', 'conductor': 1400, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[1], [1, -1, 3], [1], [1, -1], [1, 5, 11], [1, 1, 13], [1, 3, 17], [1, 6, 19], [1, -6, 23], [1, 9, 29], [1, 0, 31], [1, 6, 37], [1, -8, 41], [1, 6, 43], [1, 3, 47], [1, -12, 53], [1, -8, 59], [1, 4, 61], [1, -4, 67], [1, -8, 71], [1, 10, 73], [1, 3, 79], [1, -12, 83], [1, 16, 89], [1, 7, 97], [1, 14, 101], [1, -9, 103], [1, 2, 107], [1, 11, 109], [1, -6, 113]], 'euler_factors_factorization': [[1], [[[1, -1, 3], 1]], [1], [[[1, -1], 1]], [[[1, 5, 11], 1]], [[[1, 1, 13], 1]], [[[1, 3, 17], 1]], 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-2.463952365069562, -2.484119576235028, -2.4073540952647057, -2.2446018436137942, -2.0105318367869507, -1.7227975935361168, -1.401158403939303, -1.0665025019794483], 'positive_zeros': ['2.08175715199719083636321296262371', '2.76252169464449428978311315426366', '3.92102309478332339985108610602914', '5.02967376320291988227199382318883', '5.67002771047620563739767976210687', '6.87549713237471057055540036166098', '7.66737852056154649182867009604403', '8.462219312931430130295138543436697', '8.923791913883665586804923257642723'], 'prelabel': '2-1400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.343509575727167, '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': 496422916392847502, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.08175715199719083636321296262', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.76252169464449428978311315426', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.92102309478332339985108610603', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.179056282979259, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 1400, 'conductor_radical': 70, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 1, 0, -2, 0, -5, 0, -1, 0, 0, 0, -3, 0, -6, 0, 1, 0, 6, 0, 0, 0, -5, 0, -9, 0, 0, 0, -5, 0, 0, 0, -6, 0, -1, 0, 8, 0, -6, 0, 0, 0, -3, 0, 1, 0, -3, 0, 12, 0, 0, 0, -6, 0, 8, 0, -4, 0, -2, 0, 0, 0, 4, 0, 6, 0, 8, 0, -10, 0, 0, 0, -5, 0, -3, 0, 1, 0, 12, 0, 0, 0, -9, 0, -16, 0, -1, 0, 0, 0, 0, 0, -7, 0, 10, 0], 'euler11': [1, 5, 11], 'euler13': [1, 1, 13], 'euler17': [1, 3, 17], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, -6, 23], 'euler29': [1, 9, 29], 'euler3': [1, -1, 3], 'euler31': [1, 0, 31], 'euler37': [1, 6, 37], 'euler41': [1, -8, 41], 'euler43': [1, 6, 43], 'euler47': [1, 3, 47], 'euler5': [1, 0, 0], 'euler53': [1, -12, 53], 'euler59': [1, -8, 59], 'euler61': [1, 4, 61], 'euler67': [1, -4, 67], 'euler7': [1, -1, 0], 'euler71': [1, -8, 71], 'euler73': [1, 10, 73], 'euler79': [1, 3, 79], 'euler83': [1, -12, 83], 'euler89': [1, 16, 89], 'euler97': [1, 7, 97], 'euler_factors': [[1, 0, 0], [1, -1, 3], [1, 0, 0], [1, -1, 0], [1, 5, 11], [1, 1, 13], [1, 3, 17], [1, 6, 19], [1, -6, 23], [1, 9, 29], [1, 0, 31], [1, 6, 37], [1, -8, 41], [1, 6, 43], [1, 3, 47], [1, -12, 53], [1, -8, 59], [1, 4, 61], [1, -4, 67], [1, -8, 71], [1, 10, 73], [1, 3, 79], [1, -12, 83], [1, 16, 89], [1, 7, 97]], 'index': 25, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1400/k', 'ModularForm/GL2/Q/holomorphic/1400/2/a/k/1/1', 'ModularForm/GL2/Q/holomorphic/1400/2/a/k'], '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': '2-1400-1.1-c1-0-25', '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': '2-1400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.343509575727167, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 496422916392847502, 'z1': {'__RealLiteral__': 0, 'data': '2.08175715199719083636321296262', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20618632
{'Lhash': '2638940703258648350892128998475', 'Lhash_array': ['2638940703258648350892128998475'], 'label': '2-1400-1.1-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1400/2/a/k'}
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id: 24552970
{'Lhash': '2638940703258648350892128998475', 'Lhash_array': ['2638940703258648350892128998475'], 'label': '2-1400-1.1-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1400/2/a/k/1/1'}
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id: 36529
{'Lhash': '496422916392847502', 'Lhash_array': ['496422916392847502'], 'label': '2-1400-1.1-c1-0-25', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1400/k'}