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lfunc_lfunctions • Show schema
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{'Lhash': '1792965517160608858438229160164', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [2.302014130173181, 0], 'a6': [0, 0], 'a7': [-2.1432372443592054, 1.5513007814062236], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.1100711784264, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.1432372443592054, -1.5513007814062236]]]], 'bad_primes': [2, 3, 7], 'central_character': '2268.109', 'coefficient_field': 'CDF', 'conductor': 2268, 'conductor_radical': 42, 'conjugate': '414783723600356292749860663235', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.302014130173181, 0], [5.0, 0]], [[1.0, 0], [2.1432372443592054, -1.5513007814062236]], [[1.0, 0], [4.462909148671014, 0], [11.0, 0]], [[1.0, 0], [-1.4214817911873305, 2.46207868437047], [-6.5, -11.258330249197702]], [[1.0, 0], 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'7.51932334497364516420507375699261', '8.708844954303846439390036612093825', '9.204199519890100227814306981615695'], 'prelabel': '2-2268-63.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.255592929125905, 'root_angle': 0.5985203438957831, 'root_number': '-0.3045927075300876067228826946746793814457132138350797372 + 0.9524826940787378487293854195462393954892220118144816690*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2992601719478916', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41440040089737748040723810057', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48899143590471316417539637277', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43346747452777831602649641680', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.1100711784264, 'bad_primes': [2, 3, 7], 'central_character': '63.4', 'conductor': 2268, 'conductor_radical': 42, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2268/2/l/n/109/7'], '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': '2-2268-63.4-c1-0-25', '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': '2-2268-63.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.255592929125905, 'root_angle': 0.29926017194789156, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41440040089737748040723810057', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1792965517160608858438229160164', 'Lhash_array': ['1792965517160608858438229160164'], 'label': '2-2268-63.4-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2268/2/l/n/109/7'}