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lfunc_lfunctions • Show schema
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{'Lhash': '175903657643060868919547902815', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [1.0, 2.0], 'a6': [0, 0], 'a7': [0, 1.0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.24460261872533, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, -2.0]]], [7, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '5040.1009', 'coefficient_field': 'CDF', 'conductor': 5040, 'conductor_radical': 210, 'conjugate': '2394179358826193811125255410816', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, -2.0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [2.0, 0], [11.0, 0]], [[1.0, 0], [0, -2.0], [-13.0, 0]], [[1.0, 0], [0, -8.0], [-17.0, 0]], [[1.0, 0], [2.0, 0], [19.0, 0]], [[1.0, 0], [0, 0], [-23.0, 0]], [[1.0, 0], [6.0, 0], [29.0, 0]], [[1.0, 0], [6.0, 0], [31.0, 0]], 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4.081942292080462, 3.6714829870398287, 3.1923252265615885, 2.667027410208535, 2.1204027165229857, 1.5783314602026397, 1.0665103548876307, 0.6092007891480218, 0.22803895115737197, -0.059031843659854144, -0.23865187467921042, -0.3027125262122606, -0.24876528798307734, -0.08014985436836541, 0.19416686602305575, 0.5600342414487158, 0.998822731592903, 1.4883552138948641, 2.0040180546371884, 2.519995528897194, 3.0105644245786523, 3.4513821466449603], 'positive_zeros': ['0.13876351859999194898018041975964', '1.19493067099303979779355492197699', '2.31092564693398283615615400929095', '3.16732031872953320590923270594849', '4.21799697076741159139333303546609', '5.06548870694745889855017109044562', '5.38835197531502580602532128080184', '6.34939921314195853668822334233924', '7.23982752453284554159702095117293', '7.78637554285595287807837674701381'], 'prelabel': '2-5040-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.343863382728645, 'root_angle': 0.8524163823495667, 'root_number': '-0.89442719099991587856366946749251049417624734384461028971 + 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.42620819117478337', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.13876351859999194898018041976', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.19493067099303979779355492198', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.31092564693398283615615400929', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 40.24460261872533, 'bad_primes': [2, 3, 5, 7], 'central_character': '5.4', 'conductor': 5040, 'conductor_radical': 210, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5040/2/t/k/1009/2'], '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': '2-5040-5.4-c1-0-2', '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': '2-5040-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.343863382728645, 'root_angle': 0.42620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.13876351859999194898018041976', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '175903657643060868919547902815', 'Lhash_array': ['175903657643060868919547902815'], 'label': '2-5040-5.4-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5040/2/t/k/1009/2'}