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lfunc_lfunctions • Show schema
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{'Lhash': '2138632366027534718187797412738', 'a10': [-0.08308111054862333, 0.07471727619498109], 'a2': [0.5744451320619925, 1.2922897470189416], 'a3': [0.5877852522924731, 0.8090169943749475], 'a4': [-1.3400255805005599, 1.4846991087773096], 'a5': [0.024415415215497786, 0.07514292146203572], 'a6': [-0.707833990117584, 1.2243247291606179], 'a7': [0.5007351532249956, 0.3638053840852401], 'a8': [-2.6884326072381697, -0.8788231428100746], 'a9': [-0.30901699437494745, 0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0540253066809016, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5744451320619925, -1.2922897470189416]]], [3, [[1.0, 0], [-0.5877852522924731, -0.8090169943749475]]], [11, [[1.0, 0], [-0.08575833771855683, 3.3155158735122576]]]], 'bad_primes': [2, 3, 11], 'central_character': '132.79', 'coefficient_field': 'CDF', 'conductor': 132, 'conductor_radical': 66, 'conjugate': 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[-67.14841053312064, 48.78617594027527]], [[1.0, 0], [-3.5551885268685797, 0], [89.0, 0]], [[1.0, 0], [-4.200146374492387, 12.926721350501545], [-78.4746484543699, -57.01516947236989]], [[1.0, 0], [-7.497451837027433, -2.436069773407799], [81.71071643186968, 59.366310481539784]], [[1.0, 0], [-11.215692632249127, 15.437076564589445], [-31.828750420619585, -97.95882117840081]], [[1.0, 0], [-4.920517320726983, 3.5749650932951473], [33.06481839811937, -101.76304724358143]], [[1.0, 0], [0, -18.63986456419537], [-109.0, 0]], [[1.0, 0], [-12.998818783765003, 9.444194660240196], [34.91892036436906, -107.46938634135235]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-132-44.35-c1-0-4', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/132/2/j/a/79/8', 'plot_delta': {'__RealLiteral__': 0, 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'-0.275529421407', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.68708346419943529303624799047', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.35895493224157831147197956480', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.78165415410411891592861808238', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0540253066809016, 'bad_primes': [2, 3, 11], 'central_character': '44.35', 'conductor': 132, 'conductor_radical': 66, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/132/2/j/a/79/8'], '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': '2-132-44.35-c1-0-4', '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': '2-132-44.35-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0266573462849724, 'root_angle': -0.2755294214065643, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68708346419943529303624799047', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2138632366027534718187797412738', 'Lhash_array': ['2138632366027534718187797412738'], 'label': '2-132-44.35-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/132/2/j/a/79/8'}