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lfunc_lfunctions • Show schema
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{'Lhash': '2171775519715022649725017389892', 'a10': 2, 'a2': 1, 'a3': 0, 'a4': 1, 'a5': 2, 'a6': 0, 'a7': -2, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.53817913147007, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [17, [1]]], 'bad_primes': [2, 3, 17], 'central_character': '5202.1', 'coefficient_field': '1.1.1.1', 'conductor': 5202, 'conductor_radical': 102, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, -2, 5], [1, 2, 7], [1, 0, 11], [1, 6, 13], [1], [1, 0, 19], [1, 6, 23], [1, 6, 29], [1, -10, 31], [1, -2, 37], [1, 0, 41], [1, 4, 43], [1, 8, 47], [1, 6, 53], [1, 0, 59], [1, -10, 61], [1, -8, 67], [1, 10, 71], [1, 16, 73], [1, 6, 79], [1, 16, 83], [1, 10, 89], [1, -12, 97], [1, -18, 101], [1, 16, 103], [1, -8, 107], [1, -14, 109], [1, -4, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [1], [[[1, -2, 5], 1]], [[[1, 2, 7], 1]], [[[1, 0, 11], 1]], [[[1, 6, 13], 1]], [1], 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0.3036526058898091, 0.3440937487934015, 0.27491847687010934, 0.1071485332373878, -0.14372703765602288, -0.4586364758325115, -0.815980817005431, -1.1928039386816318, -1.5660148861303904], 'positive_zeros': ['1.71322880241922613811878747961109', '2.48419381613578824984071623625953', '3.19303306539765535110570927334719', '4.23874111677559334767471093323597', '4.92584661119087784740544299429154', '5.74812007553288254294044544159647', '6.24768185274950950215367320392426', '6.97040060408676232636930869063815', '7.67724089422182327943323233750247'], 'prelabel': '2-5202-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.44501195743422, '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': 1341725324610806850, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.71322880241922613811878747961', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48419381613578824984071623626', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.19303306539765535110570927335', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.53817913147007, 'bad_primes': [2, 3, 17], 'central_character': '1.1', 'conductor': 5202, 'conductor_radical': 102, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 2, 0, -2, 1, 0, 2, 0, 0, -6, -2, 0, 1, 0, 0, 0, 2, 0, 0, -6, 0, -1, -6, 0, -2, -6, 0, 10, 1, 0, 0, -4, 0, 2, 0, 0, 2, 0, 0, -4, 0, 0, -6, -8, 0, -3, -1, 0, -6, -6, 0, 0, -2, 0, -6, 0, 0, 10, 10, 0, 1, -12, 0, 8, 0, 0, -4, -10, 0, -16, 2, 0, 0, 0, 0, -6, 2, 0, 0, -16, 0, 0, -4, 0, 0, -10, 0, 12, -6, 0, -8, 0, 0, 12, -3, 0, -1], 'euler11': [1, 0, 11], 'euler13': [1, 6, 13], 'euler17': [1, 0, 0], 'euler19': [1, 0, 19], 'euler2': [1, -1, 0], 'euler23': [1, 6, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -10, 31], 'euler37': [1, -2, 37], 'euler41': [1, 0, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, -2, 5], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -10, 61], 'euler67': [1, -8, 67], 'euler7': [1, 2, 7], 'euler71': [1, 10, 71], 'euler73': [1, 16, 73], 'euler79': [1, 6, 79], 'euler83': [1, 16, 83], 'euler89': [1, 10, 89], 'euler97': [1, -12, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, -2, 5], [1, 2, 7], [1, 0, 11], [1, 6, 13], [1, 0, 0], [1, 0, 19], [1, 6, 23], [1, 6, 29], [1, -10, 31], [1, -2, 37], [1, 0, 41], [1, 4, 43], [1, 8, 47], [1, 6, 53], [1, 0, 59], [1, -10, 61], [1, -8, 67], [1, 10, 71], [1, 16, 73], [1, 6, 79], [1, 16, 83], [1, 10, 89], [1, -12, 97]], 'index': 109, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/5202/n', 'ModularForm/GL2/Q/holomorphic/5202/2/a/n/1/1', 'ModularForm/GL2/Q/holomorphic/5202/2/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': '2-5202-1.1-c1-0-109', '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': '2-5202-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.44501195743422, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1341725324610806850, 'z1': {'__RealLiteral__': 0, 'data': '1.71322880241922613811878747961', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21484081
{'Lhash': '2171775519715022649725017389892', 'Lhash_array': ['2171775519715022649725017389892'], 'label': '2-5202-1.1-c1-0-109', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5202/2/a/n'}
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id: 24569400
{'Lhash': '2171775519715022649725017389892', 'Lhash_array': ['2171775519715022649725017389892'], 'label': '2-5202-1.1-c1-0-109', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5202/2/a/n/1/1'}
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id: 102808
{'Lhash': '1341725324610806850', 'Lhash_array': ['1341725324610806850'], 'label': '2-5202-1.1-c1-0-109', 'type': 'ECQ', 'url': 'EllipticCurve/Q/5202/n'}