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lfunc_lfunctions • Show schema
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{'Lhash': '1770902993407534189024168982492', 'a10': [0.0, 0.0], 'a2': [0.0, -1.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 4.0], 'a8': [0.0, -3.0], 'a9': [3.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.393642085904418, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [5, 17], 'central_character': '425.324', 'coefficient_field': 'CDF', 'conductor': 425, 'conductor_radical': 85, 'conjugate': '2109563005578663171298123682510', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0], [-2.0, 0]], [[1.0, 0], [0, 0], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -4.0], [-7.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [0, -2.0], [-13.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [-4.0, 0], [19.0, 0]], [[1.0, 0], [0, 4.0], [-23.0, 0]], [[1.0, 0], [6.0, 0], [29.0, 0]], [[1.0, 0], [-4.0, 0], [31.0, 0]], [[1.0, 0], [0, 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{'__RealLiteral__': 0, 'data': '0.0737918088252', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39699613843806692195408059085', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.27421846633199865520241686865', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.50562702493167937967098019859', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.393642085904418, 'bad_primes': [5, 17], 'central_character': '5.4', 'conductor': 425, 'conductor_radical': 85, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/425/2/b/b/324/1'], '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': '2-425-5.4-c1-0-10', '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': '2-425-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8421840532108669, 'root_angle': 0.07379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39699613843806692195408059085', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1770902993407534189024168982492', 'Lhash_array': ['1770902993407534189024168982492'], 'label': '2-425-5.4-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/425/2/b/b/324/1'}