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lfunc_lfunctions • Show schema
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{'Lhash': '4197896217512276642823651360056', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -1.4142135623730951], 'a4': [0.0, 0.0], 'a5': [0.0, -2.8284271247461903], 'a6': [0.0, 0.0], 'a7': [0.0, 4.242640687119285], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5429827337447068, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-3.0, -2.8284271247461903]]]], 'bad_primes': [2, 17], 'central_character': '68.33', 'coefficient_field': 'CDF', 'conductor': 68, 'conductor_radical': 34, 'conjugate': '2565603733600319243895141520212', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.4142135623730951], [-3.0, 0]], [[1.0, 0], [0, 2.8284271247461903], [-5.0, 0]], [[1.0, 0], [0, -4.242640687119285], [-7.0, 0]], [[1.0, 0], [0, -1.4142135623730951], [-11.0, 0]], [[1.0, 0], [4.0, 0], [13.0, 0]], [[1.0, 0], [-3.0, -2.8284271247461903]], [[1.0, 0], 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'14.61407234852838053605671649477616'], 'prelabel': '2-68-17.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7368736212843467, 'root_angle': 0.12031626849523071, 'root_number': '0.7276068751089989 + 0.6859943405700354*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.120316268495', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.31155621017059602303168202463', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.64030908745122342322785253550', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.73888792302150141204335430044', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5429827337447068, 'bad_primes': [2, 17], 'central_character': '17.16', 'conductor': 68, 'conductor_radical': 34, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/68/2/b/a/33/1'], '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': '2-68-17.16-c1-0-1', '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': '2-68-17.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7368736212843467, 'root_angle': 0.12031626849523071, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.31155621017059602303168202463', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4197896217512276642823651360056', 'Lhash_array': ['4197896217512276642823651360056'], 'factors': ['2-68-17.16-c1-0-1'], 'label': '2-68-17.16-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/68/2/b/a/33/1'}