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lfunc_lfunctions • Show schema
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{'Lhash': '1127880272896002089728374725773', 'a10': [-1.1141205067144575, 1.9297133233838228], 'a2': [1.2239231447763013, 2.1198970713120326], 'a3': [-0.3337257828381452, 0.5780300116713651], 'a4': [-1.9959757286382223, 3.457131372675711], 'a5': [0.45514316461352944, 0.7883310858283181], 'a6': [-1.6338188384967829, 1.3399689494982736e-61], 'a7': [0.0, 0.0], 'a8': [-4.875990983663044, 0.0], 'a9': [1.2772542037381343, 2.2122691750553787], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [7, 13], 'central_character': '637.508', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '3235206639736098736067224971948', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.2239231447763013, -2.1198970713120326], [-1.0, 1.7320508075688772]], [[1.0, 0], [0.3337257828381452, 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'7.42144056693408264561366562973856', '8.643557519210928867061624461224585', '9.590253632991010591466616603020938', '10.40394733412138908552717050890365'], 'prelabel': '2-637-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.8967970958395212, 'root_number': '-0.9478990257184787 + 0.31857092937359927*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.44839854792', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.889740653057662034786035416057', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.04800182541080329116087102410', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43137868067861434165354849843', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '7.4', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/e/o/508/6'], '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': '2-637-7.4-c1-0-10', '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': '2-637-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.4483985479197606, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.889740653057662034786035416057', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1127880272896002089728374725773', 'Lhash_array': ['1127880272896002089728374725773'], 'label': '2-637-7.4-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/e/o/508/6'}