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lfunc_lfunctions • Show schema
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{'Lhash': '1093362768212852668849090543151', 'a10': [-3.3880282304662703, 0.0], 'a2': [-1.0, 0.0], 'a3': [-1.8744532487430174, 0.0], 'a4': [1.0, 0.0], 'a5': [3.3880282304662703, 0.0], 'a6': [1.8744532487430174, 0.0], 'a7': [0.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [0.5135749817232528, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 79.03592792066337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [101, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 7, 101], 'central_character': '9898.1', 'coefficient_field': 'CDF', 'conductor': 9898, 'conductor_radical': 1414, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [1.8744532487430174, 0], [3.0, 0]], [[1.0, 0], [-3.3880282304662703, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.768723941776364, 0], [11.0, 0]], [[1.0, 0], [-5.066045112272498, 0], [13.0, 0]], [[1.0, 0], [-1.41553540259694, 0], [17.0, 0]], [[1.0, 0], 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[11.526059906857405, 0], [109.0, 0]], [[1.0, 0], [-8.64015113188243, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 135, 'label': '2-9898-1.1-c1-0-135', 'leading_term': '1.8266523900473078203618483766994', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/9898/2/a/t/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [1.8266523900473077, 1.8197099072906133, 1.7989012396677948, 1.7642878434738507, 1.7159887737103112, 1.654204195267956, 1.579245572845371, 1.491570107789349, 1.3918166641177943, 1.280840301204948, 1.1597425902918344, 1.0298951054672902, 0.8929538105153013, 0.7508624755151454, 0.6058437212699392, 0.46037678284997435, 0.31716159020689966, 0.17906927389510155, 0.049079710736645556, -0.06979277765423454, -0.17458397708810905, 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'4.11831397283239397610636701846362', '5.48197244720942008379042635045123', '5.77181689470143402854881497544334', '6.09378632391895429591002792785891', '6.90058015666617411984021028542570', '7.43703774285019076014545172410386'], 'prelabel': '2-9898-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.890215291018738, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.862511143067342268352646750728', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.41481832490267401222041549386', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.20985112106327146213065306181', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 79.03592792066337, 'bad_primes': [2, 7, 101], 'central_character': '1.1', 'conductor': 9898, 'conductor_radical': 1414, 'degree': 2, 'index': 135, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9898/2/a/t/1/1'], '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': '2-9898-1.1-c1-0-135', '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': '2-9898-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.890215291018738, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.862511143067342268352646750728', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1093362768212852668849090543151', 'Lhash_array': ['1093362768212852668849090543151'], 'label': '2-9898-1.1-c1-0-135', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9898/2/a/t/1/1'}