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lfunc_lfunctions • Show schema
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{'Lhash': '1686423768355037364865803188023', 'a10': [-20.66972841920453, -8.53008365001941], 'a2': [-1.994904229220507, -0.14267836639846468], 'a3': [-0.14384171418581237, -0.6612296885731953], 'a4': [3.9592857675237307, 0.5692593530931406], 'a5': [10.612796760184363, 3.5168942160691], 'a6': [0.19260727218781548, 1.3396130030208127], 'a7': [-7.161576255913122, -13.115447682042275], 'a8': [-7.817174927769276, -1.7005223164238135], 'a9': [24.143529612261304, -11.025980527301096], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.570439301320347, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.994904229220507, 0.14267836639846468]]], [5, [[1.0, 0], [-10.612796760184363, -3.5168942160691]]], [23, [[1.0, 0], [10.432489507088752, -109.80966789260627]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.33', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': 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3.683807717745369, 'root_angle': 0.11603820231575257, 'root_number': '0.745781259623737 + 0.6661908981621051*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.116038202316', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33035378049078469869025023391', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.64863650272454801899173211828', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.57490735010140443210279295291', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.570439301320347, 'bad_primes': [2, 5, 23], 'central_character': '115.33', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/4/l/a/33/9'], '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': '2-230-115.33-c3-0-20', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-230-115.33-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.683807717745369, 'root_angle': 0.11603820231575257, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33035378049078469869025023391', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1686423768355037364865803188023', 'Lhash_array': ['1686423768355037364865803188023'], 'factors': ['2-230-115.33-c3-0-20'], 'label': '2-230-115.33-c3-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/4/l/a/33/9'}