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lfunc_lfunctions • Show schema
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{'Lhash': '2141862048395934536667396275139', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.7320508075688772, -1.0], 'a4': [-1.0, 1.7320508075688772], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, -4.0], 'a8': [0.0, 0.0], 'a9': [0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-3.5, 2.598076211353316]]]], 'bad_primes': [5, 19], 'central_character': '475.349', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '1597900633431204152128038001858', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [1.0, -1.7320508075688772]], [[1.0, 0], [-1.7320508075688772, 1.0], [1.5, -2.598076211353316]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 4.0], [-7.0, 0]], [[1.0, 0], [-3.0, 0], [11.0, 0]], [[1.0, 0], [-1.7320508075688772, -1.0], [6.5, 11.258330249197702]], [[1.0, 0], 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-0.3170512147189407, 0.2330322209893316, 0.5862746425778024], 'positive_zeros': ['1.68963123435614751517504654443019', '3.18598208237196360298998038067598', '4.14581044886372423467508100544424', '5.65087247543136885852418416392908', '5.96004480878040017705807850892267', '7.77464208771795972208962237531674', '8.783436304268985795564881361404622', '9.228234855902200390235690546355115', '9.844501474706357922007565514407678', '10.91381483453929153099001190198780'], 'prelabel': '2-475-95.64-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.17874370819254642, 'root_number': '0.8464361222323977 + 0.5324902731319902*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0893718540963', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.68963123435614751517504654443', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.18598208237196360298998038068', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.14581044886372423467508100544', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '95.64', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/j/a/349/2'], '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': '2-475-95.64-c1-0-20', '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': '2-475-95.64-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.08937185409627321, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68963123435614751517504654443', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2141862048395934536667396275139', 'Lhash_array': ['2141862048395934536667396275139'], 'label': '2-475-95.64-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/j/a/349/2'}