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lfunc_lfunctions • Show schema
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{'Lhash': '2643518300587997005216192648840', 'a10': [-1.0511023019022032, 0.6068541969490723], 'a2': [-0.3587194676071504, -0.20710678118654752], 'a3': [0.0, 0.0], 'a4': [-0.914213562373095, -1.5834643389987395], 'a5': [1.4650756326574836, -2.5375854326938785], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 1.5857864376269049], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '441.215', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '1036222599614020709955625654916', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.3587194676071504, 0.20710678118654752], [1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.4650756326574836, 2.5375854326938785], [-2.5, -4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], 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False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': 0.6530780509683655, 'root_number': '-0.46258515695519037 + 0.8865748544622399*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.326539025484', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.08536823957015810192403323028', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.48877780656809221776394884904', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.39230686741291378255483478267', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'bad_primes': [3, 7], 'central_character': '21.5', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/2/p/c/215/4'], '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': '2-21e2-21.5-c1-0-11', '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': '2-21e2-21.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': 0.32653902548418273, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.08536823957015810192403323028', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2643518300587997005216192648840', 'Lhash_array': ['2643518300587997005216192648840'], 'label': '2-21e2-21.5-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/2/p/c/215/4'}