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lfunc_lfunctions • Show schema
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{'Lhash': '3271335790445844730092597195649', 'a10': [1.4067806811809334e-60, 7.916334344242358], 'a2': [-2.2745303867731903, -0.40106107562937365], 'a3': [1.2260908548499303, -1.2233974070813487], 'a4': [3.133253252397791, 1.1404109202905643], 'a5': [-0.5951878732367258, -3.3754781647443735], 'a6': [-3.2794379863071157, 2.2909172604406063], 'a7': [-2.645693864834248, -0.017434838066953093], 'a8': [-2.668928394413526, -1.5409065269624849], 'a9': [0.006597568693266044, -2.9999927453391178], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5091725982022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.2260908548499303, 1.2233974070813487]]], [7, [[1.0, 0], [2.645693864834248, 0.017434838066953093]]]], 'bad_primes': [3, 7], 'central_character': '189.38', 'coefficient_field': 'CDF', 'conductor': 189, 'conductor_radical': 21, 'conjugate': '904106625224667318247594564924', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.58062891293300325642476724767', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.74603884911007646042825121788', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.25701844729181351186452976540', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5091725982022, 'bad_primes': [3, 7], 'central_character': '189.38', 'conductor': 189, 'conductor_radical': 21, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/189/2/ba/a/38/4'], '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': '2-189-189.38-c1-0-16', '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': '2-189-189.38-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2284838615961546, 'root_angle': 0.4212156787976504, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.58062891293300325642476724767', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3271335790445844730092597195649', 'Lhash_array': ['3271335790445844730092597195649'], 'label': '2-189-189.38-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/189/2/ba/a/38/4'}