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lfunc_lfunctions • Show schema
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{'Lhash': '2793769949619605084355514861041', 'a10': [0.36602540378443865, 1.3660254037844386], 'a2': [-1.3660254037844386, 0.36602540378443865], 'a3': [1.7320508075688772, 0.0], 'a4': [1.7320508075688772, -1.0], 'a5': [0.0, -1.0], 'a6': [-2.366025403784439, 0.6339745962155614], 'a7': [1.7320508075688772, -2.0], 'a8': [-2.0, 2.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1179056282979258, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3660254037844386, -0.36602540378443865]]], [5, [[1.0, 0], [0, 1.0]]], [7, [[1.0, 0], [-1.7320508075688772, 2.0]]]], 'bad_primes': [2, 5, 7], 'central_character': '140.111', 'coefficient_field': 'CDF', 'conductor': 140, 'conductor_radical': 70, 'conjugate': '2121641778605764252079683957343', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3660254037844386, -0.36602540378443865]], [[1.0, 0], [-1.7320508075688772, 0], [3.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], 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['2.20389589143618221305775567118938', '3.27145977687743645557013697797168', '5.54146860361022471232453573477117', '7.34476711637577239965022710426628', '8.009373213722982671850439819836250', '9.002827187948285875855316348388639', '9.925140027950758437894106989987579', '10.96751445537355976307273780707676', '12.06913601291104380686308904301473', '13.01279461450136737030590057380382'], 'prelabel': '2-140-28.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0573105637881075, 'root_angle': 0.060518859161838384, 'root_number': '0.9819805060619657 + 0.18898223650461365*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0302594295809', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.20389589143618221305775567119', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.27145977687743645557013697797', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.54146860361022471232453573477', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1179056282979258, 'bad_primes': [2, 5, 7], 'central_character': '28.27', 'conductor': 140, 'conductor_radical': 70, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/140/2/g/a/111/2'], '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': '2-140-28.27-c1-0-9', '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': '2-140-28.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0573105637881075, 'root_angle': 0.030259429580919192, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.20389589143618221305775567119', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2793769949619605084355514861041', 'Lhash_array': ['2793769949619605084355514861041'], 'label': '2-140-28.27-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/140/2/g/a/111/2'}