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lfunc_lfunctions • Show schema
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{'Lhash': '1055479948819122385639347052565', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-3.745781332380684, 3.745781332380684], 'a4': [0, 0], 'a5': [3.764815063457915, -3.290314200492162], 'a6': [0, 0], 'a7': [-0.026102211966934692, 6.999951333725859], 'a8': [0, 0], 'a9': [0, -19.061755580023224], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.258894804176627, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-3.764815063457915, 3.290314200492162]]], [7, [[1.0, 0], [0.026102211966934692, -6.999951333725859]]]], 'bad_primes': [2, 5, 7], 'central_character': '560.447', 'coefficient_field': 'CDF', 'conductor': 560, 'conductor_radical': 70, 'conjugate': '1344429208222788853381966456416', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.745781332380684, -3.745781332380684], [0, -9.0]], [[1.0, 0], [-3.764815063457915, 3.290314200492162]], [[1.0, 0], [0.026102211966934692, 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'0.2981059045253873575212130041527613383022517975089572882 - 0.9545328017868744972425163661752388869973056002339779582*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.201822569942249', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.832626867868080095505607421474', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.83466532893422729369447905456', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51490740789041723930063090696', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.258894804176627, 'bad_primes': [2, 5, 7], 'central_character': '140.27', 'conductor': 560, 'conductor_radical': 70, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/560/3/v/a/447/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-560-140.27-c2-0-21', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-560-140.27-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9062635349111594, 'root_angle': -0.201822569942249, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.832626867868080095505607421474', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1055479948819122385639347052565', 'Lhash_array': ['1055479948819122385639347052565'], 'factors': ['2-560-140.27-c2-0-21'], 'label': '2-560-140.27-c2-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/560/3/v/a/447/2'}